1.
Phase (matter)
–
In the physical sciences, a phase is a region of space, throughout which all physical properties of a material are essentially uniform. Examples of physical properties include density, index of refraction, magnetization, a simple description is that a phase is a region of material that is chemically uniform, physically distinct, and mechanically separable. In a system consisting of ice and water in a jar, the ice cubes are one phase, the water is a second phase. The glass of the jar is another separate phase, the term phase is sometimes used as a synonym for state of matter, but there can be several immiscible phases of the same state of matter. Also, the phase is sometimes used to refer to a set of equilibrium states demarcated in terms of state variables such as pressure and temperature by a phase boundary on a phase diagram. Distinct phases may be described as different states of such as gas, liquid, solid. Useful mesophases between solid and liquid form other states of matter, distinct phases may also exist within a given state of matter. As shown in the diagram for iron alloys, several phases exist for both the solid and liquid states, phases may also be differentiated based on solubility as in polar or non-polar. A mixture of water and oil will separate into two phases. Water has a low solubility in oil, and oil has a low solubility in water. Solubility is the amount of a solute that can dissolve in a solvent before the solute ceases to dissolve. A mixture can separate into more than two phases and the concept of phase separation extends to solids, i. e. solids can form solid solutions or crystallize into distinct crystal phases. Metal pairs that are mutually soluble can form alloys, whereas metal pairs that are mutually insoluble cannot, as many as eight immiscible liquid phases have been observed. Mutually immiscible liquid phases are formed from water, hydrophobic solvents, perfluorocarbons, silicones, several different metals. Not all organic solvents are completely miscible, e. g. a mixture of ethylene glycol, phases do not need to macroscopically separate spontaneously. Emulsions and colloids are examples of immiscible phase pair combinations that do not physically separate, left to equilibration, many compositions will form a uniform single phase, but depending on the temperature and pressure even a single substance may separate into two or more distinct phases. Within each phase, the properties are uniform but between the two phases properties differ, water in a closed jar with an air space over it forms a two phase system. Most of the water is in the phase, where it is held by the mutual attraction of water molecules
2.
Phase transition
–
The term phase transition is most commonly used to describe transitions between solid, liquid and gaseous states of matter, and, in rare cases, plasma. A phase of a system and the states of matter have uniform physical properties. For example, a liquid may become gas upon heating to the boiling point, the measurement of the external conditions at which the transformation occurs is termed the phase transition. Phase transitions are common in nature and used today in many technologies, the same process, but beginning with a solid instead of a liquid is called a eutectoid transformation. A peritectic transformation, in which a two component single phase solid is heated and transforms into a phase and a liquid phase. A spinodal decomposition, in which a phase is cooled. Transition to a mesophase between solid and liquid, such as one of the crystal phases. The transition between the ferromagnetic and paramagnetic phases of materials at the Curie point. The transition between differently ordered, commensurate or incommensurate, magnetic structures, such as in cerium antimonide, the martensitic transformation which occurs as one of the many phase transformations in carbon steel and stands as a model for displacive phase transformations. Changes in the structure such as between ferrite and austenite of iron. Order-disorder transitions such as in alpha-titanium aluminides, the dependence of the adsorption geometry on coverage and temperature, such as for hydrogen on iron. The emergence of superconductivity in certain metals and ceramics when cooled below a critical temperature, the superfluid transition in liquid helium is an example of this. The breaking of symmetries in the laws of physics during the history of the universe as its temperature cooled. Isotope fractionation occurs during a transition, the ratio of light to heavy isotopes in the involved molecules changes. When water vapor condenses, the heavier water isotopes become enriched in the liquid phase while the lighter isotopes tend toward the vapor phase, Phase transitions occur when the thermodynamic free energy of a system is non-analytic for some choice of thermodynamic variables. This condition generally stems from the interactions of a number of particles in a system. It is important to note that phase transitions can occur and are defined for non-thermodynamic systems, examples include, quantum phase transitions, dynamic phase transitions, and topological phase transitions. In these types of other parameters take the place of temperature
3.
State of matter
–
In physics, a state of matter is one of the distinct forms that matter takes on. Four states of matter are observable in everyday life, solid, liquid, gas, some other states are believed to be possible but remain theoretical for now. For a complete list of all states of matter, see the list of states of matter. Historically, the distinction is based on qualitative differences in properties. Matter in the state maintains a fixed volume and shape, with component particles close together. Matter in the state maintains a fixed volume, but has a variable shape that adapts to fit its container. Its particles are close together but move freely. Matter in the state has both variable volume and shape, adapting both to fit its container. Its particles are close together nor fixed in place. Matter in the state has variable volume and shape, but as well as neutral atoms, it contains a significant number of ions and electrons. Plasma is the most common form of matter in the universe. The term phase is used as a synonym for state of matter. In a solid the particles are packed together. The forces between particles are strong so that the particles move freely but can only vibrate. As a result, a solid has a stable, definite shape, solids can only change their shape by force, as when broken or cut. In crystalline solids, the particles are packed in a regularly ordered, there are various different crystal structures, and the same substance can have more than one structure. For example, iron has a cubic structure at temperatures below 912 °C. Ice has fifteen known crystal structures, or fifteen solid phases, glasses and other non-crystalline, amorphous solids without long-range order are not thermal equilibrium ground states, therefore they are described below as nonclassical states of matter
4.
Solid
–
Solid is one of the four fundamental states of matter. It is characterized by structural rigidity and resistance to changes of shape or volume, unlike a liquid, a solid object does not flow to take on the shape of its container, nor does it expand to fill the entire volume available to it like a gas does. The atoms in a solid are tightly bound to other, either in a regular geometric lattice or irregularly. The branch of physics deals with solids is called solid-state physics. Materials science is concerned with the physical and chemical properties of solids. Solid-state chemistry is concerned with the synthesis of novel materials, as well as the science of identification. The atoms, molecules or ions which make up solids may be arranged in a repeating pattern. Materials whose constituents are arranged in a regular pattern are known as crystals, in some cases, the regular ordering can continue unbroken over a large scale, for example diamonds, where each diamond is a single crystal. Almost all common metals, and many ceramics, are polycrystalline, in other materials, there is no long-range order in the position of the atoms. These solids are known as amorphous solids, examples include polystyrene, whether a solid is crystalline or amorphous depends on the material involved, and the conditions in which it was formed. Solids which are formed by slow cooling will tend to be crystalline, likewise, the specific crystal structure adopted by a crystalline solid depends on the material involved and on how it was formed. While many common objects, such as an ice cube or a coin, are chemically identical throughout, for example, a typical rock is an aggregate of several different minerals and mineraloids, with no specific chemical composition. Wood is an organic material consisting primarily of cellulose fibers embedded in a matrix of organic lignin. In materials science, composites of more than one constituent material can be designed to have desired properties, the forces between the atoms in a solid can take a variety of forms. For example, a crystal of sodium chloride is made up of sodium and chlorine. In diamond or silicon, the atoms share electrons and form covalent bonds, in metals, electrons are shared in metallic bonding. Some solids, particularly most organic compounds, are together with van der Waals forces resulting from the polarization of the electronic charge cloud on each molecule. The dissimilarities between the types of solid result from the differences between their bonding, metals typically are strong, dense, and good conductors of both electricity and heat
5.
Liquid
–
A liquid is a nearly incompressible fluid that conforms to the shape of its container but retains a constant volume independent of pressure. As such, it is one of the four states of matter. A liquid is made up of tiny vibrating particles of matter, such as atoms, water is, by far, the most common liquid on Earth. Like a gas, a liquid is able to flow and take the shape of a container, most liquids resist compression, although others can be compressed. Unlike a gas, a liquid does not disperse to fill every space of a container, a distinctive property of the liquid state is surface tension, leading to wetting phenomena. The density of a liquid is usually close to that of a solid, therefore, liquid and solid are both termed condensed matter. On the other hand, as liquids and gases share the ability to flow, although liquid water is abundant on Earth, this state of matter is actually the least common in the known universe, because liquids require a relatively narrow temperature/pressure range to exist. Most known matter in the universe is in form as interstellar clouds or in plasma form within stars. Liquid is one of the four states of matter, with the others being solid, gas. Unlike a solid, the molecules in a liquid have a greater freedom to move. The forces that bind the molecules together in a solid are only temporary in a liquid, a liquid, like a gas, displays the properties of a fluid. A liquid can flow, assume the shape of a container, if liquid is placed in a bag, it can be squeezed into any shape. These properties make a suitable for applications such as hydraulics. Liquid particles are bound firmly but not rigidly and they are able to move around one another freely, resulting in a limited degree of particle mobility. As the temperature increases, the vibrations of the molecules causes distances between the molecules to increase. When a liquid reaches its point, the cohesive forces that bind the molecules closely together break. If the temperature is decreased, the distances between the molecules become smaller, only two elements are liquid at standard conditions for temperature and pressure, mercury and bromine. Four more elements have melting points slightly above room temperature, francium, caesium, gallium and rubidium, metal alloys that are liquid at room temperature include NaK, a sodium-potassium metal alloy, galinstan, a fusible alloy liquid, and some amalgams
6.
Gas
–
Gas is one of the four fundamental states of matter. A pure gas may be made up of atoms, elemental molecules made from one type of atom. A gas mixture would contain a variety of pure gases much like the air, what distinguishes a gas from liquids and solids is the vast separation of the individual gas particles. This separation usually makes a colorless gas invisible to the human observer, the interaction of gas particles in the presence of electric and gravitational fields are considered negligible as indicated by the constant velocity vectors in the image. One type of commonly known gas is steam, the gaseous state of matter is found between the liquid and plasma states, the latter of which provides the upper temperature boundary for gases. Bounding the lower end of the temperature scale lie degenerative quantum gases which are gaining increasing attention, high-density atomic gases super cooled to incredibly low temperatures are classified by their statistical behavior as either a Bose gas or a Fermi gas. For a comprehensive listing of these states of matter see list of states of matter. The only chemical elements which are stable multi atom homonuclear molecules at temperature and pressure, are hydrogen, nitrogen and oxygen. These gases, when grouped together with the noble gases. Alternatively they are known as molecular gases to distinguish them from molecules that are also chemical compounds. The word gas is a neologism first used by the early 17th-century Flemish chemist J. B. van Helmont, according to Paracelsuss terminology, chaos meant something like ultra-rarefied water. An alternative story is that Van Helmonts word is corrupted from gahst and these four characteristics were repeatedly observed by scientists such as Robert Boyle, Jacques Charles, John Dalton, Joseph Gay-Lussac and Amedeo Avogadro for a variety of gases in various settings. Their detailed studies ultimately led to a relationship among these properties expressed by the ideal gas law. Gas particles are separated from one another, and consequently have weaker intermolecular bonds than liquids or solids. These intermolecular forces result from interactions between gas particles. Like-charged areas of different gas particles repel, while oppositely charged regions of different gas particles attract one another, transient, randomly induced charges exist across non-polar covalent bonds of molecules and electrostatic interactions caused by them are referred to as Van der Waals forces. The interaction of these forces varies within a substance which determines many of the physical properties unique to each gas. A comparison of boiling points for compounds formed by ionic and covalent bonds leads us to this conclusion, the drifting smoke particles in the image provides some insight into low pressure gas behavior
7.
Bose gas
–
An ideal Bose gas is a quantum-mechanical phase of matter, analogous to a classical ideal gas. It is composed of bosons, which have a value of spin. This condensate is known as a Bose–Einstein condensate, the thermodynamics of an ideal Bose gas is best calculated using the grand partition function. All thermodynamic quantities may be derived from the partition function. All partial derivatives are taken with respect to one of three variables while the other two are held constant. It is more convenient to deal with the grand potential defined as. For example, for a massive Bose gas in a box, α=3/2, for a massive Bose gas in a harmonic trap we will have α=3 and the critical energy is given by,1 α = f 3 where V=mω2r2/2 is the harmonic potential. It is seen that Ec is a function of volume only, the solution is, Ω ≈ − Li α +1 α. The problem with this continuum approximation for a Bose gas is that the state has been effectively ignored. This inaccuracy becomes serious when dealing with the Bose–Einstein condensate and will be dealt with in the next section, the problem here is that the Thomas–Fermi approximation has set the degeneracy of the ground state to zero, which is wrong. There is no state to accept the condensate and so the equation breaks down. Figure 1 shows the results of the solution to this equation for α=3/2, the solid black line is the fraction of excited states 1-N0/N for N =10,000 and the dotted black line is the solution for N =1000. The blue lines are the fraction of condensed particles N0/N The red lines plot values of the negative of the chemical potential μ, as the number of particles increases, the condensed and excited fractions tend towards a discontinuity at the critical temperature. From these expansions, we can find the behavior of the gas near T =0, in particular, we are interested in the limit as N approaches infinity, which can be easily determined from these expansions. The following table lists various thermodynamic quantities calculated in the limit of low temperature and high temperature, an equal sign indicates an exact result, while an approximation symbol indicates that only the first few terms of a series in τ α is shown. It is seen that all quantities approach the values for an ideal gas in the limit of large temperature. The above values can be used to calculate other thermodynamic quantities, in one dimension bosons with delta interaction behave as fermions, they obey Pauli exclusion principle. In one dimension Bose gas with delta interaction can be solved exactly by Bethe ansatz, the bulk free energy and thermodynamic potentials were calculated by Chen Nin Yang
8.
Fermi gas
–
A Fermi gas is a phase of matter which is an ensemble of a large number of fermions. Fermions are particles that obey Fermi–Dirac statistics, by the Pauli exclusion principle, no quantum state can be occupied by more than one fermion with an identical set of quantum numbers. Thus a non-interacting Fermi gas, unlike a Bose gas, is prohibited from condensing into a Bose–Einstein condensate, for this reason, the pressure of a Fermi gas is non-zero even at zero temperature, in contrast to that of a classical ideal gas. This so-called degeneracy pressure stabilizes a neutron star or a dwarf star against the inward pull of gravity. Only when a star is massive to overcome the degeneracy pressure can it collapse into a singularity. It is possible to define a Fermi temperature below which the gas can be considered degenerate and this temperature depends on the mass of the fermions and the density of energy states. For metals, the electron gass Fermi temperature is generally many thousands of kelvins, the maximum energy of the fermions at zero temperature is called the Fermi energy. The Fermi energy surface in space is known as the Fermi surface. An ideal Fermi gas or free Fermi gas is a model assuming a collection of non-interacting fermions. It is the mechanical version of an ideal gas, for the case of fermionic particles. The behavior of electrons in a dwarf or neutrons in a neutron star can be approximated by treating them as an ideal Fermi gas. Something similar can be done for periodic systems, such as moving in the crystal lattice of metals and semiconductors. As such, it is still relatively tractable and forms the point for more advanced theories that deal with interactions. Hence, the chemical potential, µ-E0, is approximately equal to the Fermi energy at temperatures that are much lower than the characteristic Fermi temperature EF/k. The characteristic temperature is on the order of 105 K for a metal, hence at room temperature, Fermi liquid Bose gas Free electron model Gas in a box
9.
Fermi liquid
–
Fermi liquid theory is a theoretical model of interacting fermions that describes the normal state of most metals at sufficiently low temperatures. The interaction between the particles of the system does not need to be small. The theory explains why some of the properties of an interacting fermion system are similar to those of the Fermi gas. Important examples of where Fermi liquid theory has successfully applied are most notably electrons in most metals. Liquid He-3 is a Fermi liquid at low temperatures He-3 is an isotope of helium, because there is an odd number of fermions inside the nucleus, the atom itself is also a fermion. The electrons in a normal metal also form a Fermi liquid, strontium ruthenate displays some key properties of Fermi liquids, despite being a strongly correlated material, and is compared with high temperature superconductors like cuprates. The key ideas behind Landaus theory are the notion of adiabaticity, consider a non-interacting fermion system, and suppose we turn on the interaction slowly. Landau argued that in this situation, the state of the Fermi gas would adiabatically transform into the ground state of the interacting system. By Paulis exclusion principle, the ground state Ψ0 of a Fermi gas consists of fermions occupying all momentum states corresponding to momentum p < p F with all higher momentum states unoccupied. Thus, there is a correspondence between the elementary excitations of a Fermi gas system and a Fermi liquid system. In the context of Fermi liquids, these excitations are called quasi-particles, for this system, the Greens function can be written in the form G ≈ Z ω + μ − ϵ where μ is the chemical potential and ϵ is the energy corresponding to the given momentum state. The value Z is called the residue and is very characteristic of Fermi liquid theory. The spectral function for the system can be observed via ARPES experiment. These dressed fermions are what we think of as quasiparticles, another important property of Fermi liquids is related to the scattering cross section for electrons. Suppose we have an electron with energy ϵ1 above the Fermi surface and this reduces the phase space volume of the possible states after scattering, and hence, by Fermis golden rule, the scattering cross section goes to zero. Thus we can say that the lifetime of particles at the Fermi surface goes to infinity, physically these may be thought of as being particles whose motion is disturbed by the surrounding particles and which themselves perturb the particles in their vicinity. Each many-particle excited state of the system may be described by listing all occupied momentum states. As a consequence, quantities such as the capacity of the Fermi liquid behave qualitatively in the same way as in the Fermi gas
10.
Supersolid
–
A supersolid is a spatially ordered material with superfluid properties. Superfluidity is a quantum state of matter in which a substance flows with zero viscosity. The superfluid motion of pairs of electrons within a metallic lattice is also the mechanism behind superconductivity. Superfluidity in helium arises from the liquid by a second-order phase transition. In a dilute gas of Bose particles it comes about by a transition that belongs to the universality class of the spherical model. In thin liquid helium films, it arises from the liquid by a Kosterlitz-Thouless transition. In the case of helium-4, it has been conjectured since 1970 that it might be possible to create a supersolid, in most theories of this state, it is supposed that vacancies, empty sites normally occupied by particles in an ideal crystal, exist even at absolute zero. These vacancies are caused by zero-point energy, which causes them to move from site to site as waves. A coherent flow of vacancies is equivalent to a superflow of particles in the opposite direction, despite the presence of the gas of vacancies, the ordered structure of a crystal is maintained, although with less than one particle on each lattice site on average. While several experiments yielded negative results, in the 1980s, John Goodkind from UCSD discovered the first anomaly in a solid by using ultrasound, inspired by his observation, Eun-Seong Kim and Moses Chan at Pennsylvania State University saw phenomena which were interpreted as supersolid behavior. If such an interpretation is correct, it would signify the discovery of a new phase of matter. The experiment of Kim and Chan looked for superflow by means of a torsional oscillator, to achieve this, a turntable is attached tightly to a spring-loaded spindle, then, instead of rotating at constant speed, the turntable is given an initial motion in one direction. The spring causes the table to oscillate similarly to a balance wheel, a toroid filled with solid helium-4 is attached to the table. The rate of oscillation of the turntable and toroid depend on the amount of moving with it. If there is frictionless superfluid inside, then the mass moving with the doughnut is less, in this way, one can measure the amount of superfluid existing at various temperatures. Kim and Chan found that up to about 2% of the material in the doughnut was superfluid, similar experiments in other laboratories have confirmed these results. A mysterious feature, not in agreement with the old theories, is that the continues to occur at high pressures. High-precision measurements of the pressure of helium-4 have not resulted in any observation of a phase transition in the solid
11.
Superfluidity
–
Superfluidity is the characteristic property of a fluid with zero viscosity which therefore flows without loss of kinetic energy. When stirred a superfluid forms cellular vortices that continue to rotate indefinitely, superfluidity occurs in two isotopes of helium when they are liquified by cooling to cryogenic temperatures. It is also a property of other exotic states of matter theorized to exist in astrophysics, high-energy physics. Superfluidity was originally discovered in liquid helium, by Pyotr Kapitsa and it has since been described through phenomenology and microscopic theories. In liquid helium-4, the superfluidity occurs at far higher temperatures than it does in helium-3, each atom of helium-4 is a boson particle, by virtue of its integer spin. A helium-3 atom is a particle, it can form bosons only by pairing with itself at much lower temperatures. The discovery of superfluidity in helium-3 was the basis for the award of the 1996 Nobel Prize in Physics and this process is similar to the electron pairing in superconductivity. Superfluidity in an ultracold fermionic gas was experimentally proven by Wolfgang Ketterle, such vortices had previously been observed in an ultracold bosonic gas using 87Rb in 2000, and more recently in two-dimensional gases. As early as 1999 Lene Hau created such a condensate using sodium atoms for the purpose of slowing light, with a double light-roadblock setup, we can generate controlled collisions between shock waves resulting in completely unexpected, nonlinear excitations. We have observed hybrid structures consisting of vortex rings embedded in dark solitonic shells, the vortex rings act as phantom propellers leading to very rich excitation dynamics. The idea that superfluidity exists inside neutron stars was first proposed by Arkady Migdal, superfluid vacuum theory is an approach in theoretical physics and quantum mechanics where the physical vacuum is viewed as superfluid. The ultimate goal of the approach is to develop scientific models that unify quantum mechanics with gravity and this makes SVT a candidate for the theory of quantum gravity and an extension of the Standard Model. Boojum Condensed matter physics Macroscopic quantum phenomena Quantum hydrodynamics Slow light Supersolid Guénault, annett, James F. Superconductivity, superfluids, and condensates. The Universe in a helium droplet
12.
Luttinger liquid
–
A Tomonaga-Luttinger liquid, more often referred to as simply a Luttinger liquid, is a theoretical model describing interacting electrons in a one-dimensional conductor. Such a model is necessary as the commonly used Fermi liquid model breaks down for one dimension, the Tomonaga-Luttinger liquid was first proposed by Tomonaga in 1950. The model showed that certain constraints, second-order interactions between electrons could be modelled as bosonic interactions. But his solution of the model was incorrect, the solution was given by Mattis. Luttinger liquid theory describes low energy excitations in a 1D electron gas as bosons, the completed bosonization can then be used to predict spin-charge separation. Electron-electron interactions can be treated to calculate correlation functions, for a non-interacting system, this wave velocity is equal to the Fermi velocity, while it is higher for repulsive interactions among the fermions. Likewise, there are spin density waves and these propagate independently from the charge density waves. This fact is known as spin-charge separation, charge and spin waves are the elementary excitations of the Luttinger liquid, unlike the quasiparticles of the Fermi liquid. The mathematical description becomes very simple in terms of these waves, see bosonization for one technique used. Even at zero temperature, the momentum distribution function does not display a sharp jump. There is no quasiparticle peak in the momentum-dependent spectral function, instead, there is a power-law singularity, with a non-universal exponent that depends on the interaction strength. At small temperatures, the scattering of these Friedel oscillations becomes so efficient that the strength of the impurity is renormalized to infinity. More precisely, the conductance becomes zero as temperature and transport voltage go to zero, likewise, the tunneling rate into a Luttinger liquid is suppressed to zero at low voltages and temperatures, as a power law. The Luttinger model is thought to describe the universal low-frequency/long-wavelength behaviour of any system of interacting fermions. Fermi liquid Mastropietro, Vieri, Mattis, Daniel C, Luttinger Model, The First 50 Years and Some New Directions. S. Tomonaga, Progress in Theoretical Physics,5,544 J. M. Luttinger, Lieb, Journal of Mathematical Physics,6,304 Haldane, F. D. M. Luttinger liquid theory of quantum fluids
13.
Electronic band structure
–
In solid-state physics, the electronic band structure of a solid describes the range of energies that an electron within the solid may have and ranges of energy that it may not have. Band theory derives these bands and band gaps by examining the allowed quantum mechanical wave functions for an electron in a large, the electrons of a single, isolated atom occupy atomic orbitals each of which has a discrete energy level. When two atoms together to form into a molecule, their atomic orbitals overlap. The Pauli exclusion principle dictates that no two electrons can have the quantum numbers in a molecule. Similarly if a large number N of identical atoms come together to form a solid, such as a crystal lattice, the atoms atomic orbitals overlap. Since the number of atoms in a piece of solid is a very large number the number of orbitals is very large. The energy of adjacent levels is so close together that they can be considered as a continuum and this formation of bands is mostly a feature of the outermost electrons in the atom, which are the ones responsible for chemical bonding and electrical conductivity. The inner electron orbitals do not overlap to a significant degree, Band gaps are essentially leftover ranges of energy not covered by any band, a result of the finite widths of the energy bands. The bands have different widths, with the widths depending upon the degree of overlap in the atomic orbitals from which they arise, two adjacent bands may simply not be wide enough to fully cover the range of energy. For example, the associated with core orbitals are extremely narrow due to the small overlap between adjacent atoms. As a result, there tend to be large band gaps between the core bands, higher bands involve comparatively larger orbitals with more overlap, becoming progressively wider at higher energies so that there are no band gaps at higher energies. Band theory is only an approximation to the state of a solid. These are the necessary for band theory to be valid, Infinite-size system, For the bands to be continuous. Since a macroscopic piece of material contains on the order of 1022 atoms, with modifications, the concept of band structure can also be extended to systems which are only large along some dimensions, such as two-dimensional electron systems. Homogeneous system, Band structure is a property of a material. Practically, this means that the makeup of the material must be uniform throughout the piece. Non-interactivity, The band structure describes single electron states, the existence of these states assumes that the electrons travel in a static potential without dynamically interacting with lattice vibrations, other electrons, photons, etc. Not only are there local small-scale disruptions, but also local charge imbalances and these charge imbalances have electrostatic effects that extend deeply into semiconductors, insulators, and the vacuum
14.
Plasma (physics)
–
Plasma is one of the four fundamental states of matter, the others being solid, liquid, and gas. Yet unlike these three states of matter, plasma does not naturally exist on the Earth under normal surface conditions, the term was first introduced by chemist Irving Langmuir in the 1920s. However, true plasma production is from the separation of these ions and electrons that produces an electric field. Based on the environmental temperature and density either partially ionised or fully ionised forms of plasma may be produced. The positive charge in ions is achieved by stripping away electrons from atomic nuclei, the number of electrons removed is related to either the increase in temperature or the local density of other ionised matter. Plasma may be the most abundant form of matter in the universe, although this is currently tentative based on the existence. Plasma is mostly associated with the Sun and stars, extending to the rarefied intracluster medium, Plasma was first identified in a Crookes tube, and so described by Sir William Crookes in 1879. The nature of the Crookes tube cathode ray matter was identified by British physicist Sir J. J. The term plasma was coined by Irving Langmuir in 1928, perhaps because the glowing discharge molds itself to the shape of the Crookes tube and we shall use the name plasma to describe this region containing balanced charges of ions and electrons. Plasma is a neutral medium of unbound positive and negative particles. Although these particles are unbound, they are not ‘free’ in the sense of not experiencing forces, in turn this governs collective behavior with many degrees of variation. The average number of particles in the Debye sphere is given by the plasma parameter, bulk interactions, The Debye screening length is short compared to the physical size of the plasma. This criterion means that interactions in the bulk of the plasma are more important than those at its edges, when this criterion is satisfied, the plasma is quasineutral. Plasma frequency, The electron plasma frequency is compared to the electron-neutral collision frequency. When this condition is valid, electrostatic interactions dominate over the processes of ordinary gas kinetics, for plasma to exist, ionization is necessary. The term plasma density by itself refers to the electron density, that is. The degree of ionization of a plasma is the proportion of atoms that have lost or gained electrons, even a partially ionized gas in which as little as 1% of the particles are ionized can have the characteristics of a plasma. The degree of ionization, α, is defined as α = n i n i + n n, where n i is the number density of ions and n n is the number density of neutral atoms
15.
Insulator (electricity)
–
An electrical insulator is a material whose internal electric charges do not flow freely, very little electric current will flow through it under the influence of an electric field. This contrasts with other materials, semiconductors and conductors, which conduct electric current more easily, the property that distinguishes an insulator is its resistivity, insulators have higher resistivity than semiconductors or conductors. A perfect insulator does not exist, because even insulators contain small numbers of mobile charges which can carry current, in addition, all insulators become electrically conductive when a sufficiently large voltage is applied that the electric field tears electrons away from the atoms. This is known as the voltage of an insulator. Some materials such as glass, paper and Teflon, which have high resistivity, are good electrical insulators. Examples include rubber-like polymers and most plastics which can be thermoset or thermoplastic in nature, insulators are used in electrical equipment to support and separate electrical conductors without allowing current through themselves. An insulating material used in bulk to wrap electrical cables or other equipment is called insulation, the term insulator is also used more specifically to refer to insulating supports used to attach electric power distribution or transmission lines to utility poles and transmission towers. They support the weight of the suspended wires without allowing the current to flow through the tower to ground, electrical insulation is the absence of electrical conduction. Electronic band theory says that a charge flows if states are available into which electrons can be excited and this allows electrons to gain energy and thereby move through a conductor such as a metal. If no such states are available, the material is an insulator, most insulators have a large band gap. This occurs because the valence band containing the highest energy electrons is full, there is always some voltage that gives electrons enough energy to be excited into this band. Once this voltage is exceeded the material ceases being an insulator, however, it is usually accompanied by physical or chemical changes that permanently degrade the materials insulating properties. Materials that lack electron conduction are insulators if they lack other mobile charges as well, for example, if a liquid or gas contains ions, then the ions can be made to flow as an electric current, and the material is a conductor. Electrolytes and plasmas contain ions and act as conductors whether or not electron flow is involved, when subjected to a high enough voltage, insulators suffer from the phenomenon of electrical breakdown. These freed electrons and ions are in turn accelerated and strike other atoms, creating more charge carriers, rapidly the insulator becomes filled with mobile charge carriers, and its resistance drops to a low level. In a solid, the voltage is proportional to the band gap energy. The air in a region around a conductor can break down and ionise without a catastrophic increase in current. Even a vacuum can suffer a sort of breakdown, but in case the breakdown or vacuum arc involves charges ejected from the surface of metal electrodes rather than produced by the vacuum itself
16.
Semiconductor
–
Semiconductors are crystalline or amorphous solids with distinct electrical characteristics. They are of high electrical resistance — higher than typical resistance materials and their resistance decreases as their temperature increases, which is behavior opposite to that of a metal. The behavior of charge carriers which include electrons, ions and electron holes at these junctions is the basis of diodes, transistors and all modern electronics. Semiconductor devices can display a range of properties such as passing current more easily in one direction than the other, showing variable resistance. The modern understanding of the properties of a semiconductor relies on quantum physics to explain the movement of carriers in a crystal lattice. Doping greatly increases the number of carriers within the crystal. When a doped semiconductor contains mostly free holes it is called p-type, the semiconductor materials used in electronic devices are doped under precise conditions to control the concentration and regions of p- and n-type dopants. A single semiconductor crystal can have many p- and n-type regions, although some pure elements and many compounds display semiconductor properties, silicon, germanium, and compounds of gallium are the most widely used in electronic devices. Elements near the so-called metalloid staircase, where the metalloids are located on the table, are usually used as semiconductors. Some of the properties of materials were observed throughout the mid 19th. The first practical application of semiconductors in electronics was the 1904 development of the Cats-whisker detector, developments in quantum physics in turn allowed the development of the transistor in 1947 and the integrated circuit in 1958. There are several developed techniques that allow semiconducting materials to behave like conducting materials and these modifications have two outcomes, n-type and p-type. These refer to the excess or shortage of electrons, respectively, an unbalanced number of electrons would cause a current to flow through the material. Heterojunctions Heterojunctions occur when two differently doped semiconducting materials are joined together, for example, a configuration could consist of p-doped and n-doped germanium. This results in an exchange of electrons and holes between the differently doped semiconducting materials, the n-doped germanium would have an excess of electrons, and the p-doped germanium would have an excess of holes. The transfer occurs until equilibrium is reached by a process called recombination, a product of this process is charged ions, which result in an electric field. Excited Electrons A difference in electric potential on a material would cause it to leave thermal equilibrium. This introduces electrons and holes to the system, which interact via a process called ambipolar diffusion, whenever thermal equilibrium is disturbed in a semiconducting material, the amount of holes and electrons changes
17.
Semimetal
–
A semimetal is a material with a very small overlap between the bottom of the conduction band and the top of the valence band. According to electronic band theory, solids can be classified as insulators, semiconductors, semimetals, in insulators and semiconductors the filled valence band is separated from an empty conduction band by a band gap. For insulators, the magnitude of the gap is larger than that of a semiconductor. Metals have a partially filled conduction band, a semimetal is a material with a very small overlap between the bottom of the conduction band and the top of the valence band. A semimetal thus has no band gap and a density of states at the Fermi level. A metal, by contrast, has a density of states at the Fermi level because the conduction band is partially filled. The insulating/semiconducting states differ from the states in the temperature dependency of their electrical conductivity. With a metal, the conductivity decreases with increases in temperature, with an insulator or semiconductor, both the carrier mobilities and carrier concentrations will contribute to the conductivity and these have different temperature dependencies. The semimetallic state is similar to the state but in semimetals both holes and electrons contribute to electrical conduction. To classify semiconductors and semimetals, the energies of their filled, according to the Bloch theorem the conduction of electrons depends on the periodicity of the crystal lattice in different directions. In a semimetal, the bottom of the band is typically situated in a different part of momentum space than the top of the valence band. One could say that a semimetal is a semiconductor with an indirect bandgap. Schematically, the figure shows A) a semiconductor with a direct gap B) a semiconductor with an indirect gap C) a semimetal, the figure is schematic, showing only the lowest-energy conduction band and the highest-energy valence band in one dimension of momentum space. In typical solids, k-space is three-dimensional, and there are a number of bands. Unlike a regular metal, semimetals have charge carriers of both types, so one could also argue that they should be called double-metals rather than semimetals. However, the charge carriers typically occur in smaller numbers than in a real metal. In this respect they resemble degenerate semiconductors more closely and this explains why the electrical properties of semimetals are partway between those of metals and semiconductors. As semimetals have charge carriers than metals, they typically have lower electrical and thermal conductivities
18.
Electrical conductor
–
In physics and electrical engineering, a conductor is an object or type of material that allows the flow of an electrical current in one or more directions. Materials made of metal are common electrical conductors, Electrical current is generated by the flow of negatively charged electrons, positively charged holes, and positive or negative ions in some cases. In order for current to flow, it is not necessary for one charged particle to travel from the producing the current to that consuming it. Instead, the particle simply needs to nudge its neighbor a finite amount who will nudge its neighbor and on and on until a particle is nudged into the consumer. Essentially what is occurring here is a chain of momentum transfer between mobile charge carriers, the Drude model of conduction describes this process more rigorously. Insulators are non-conducting materials with few mobile charges that support only insignificant electric currents, the resistance of a given conductor depends on the material it is made of, and on its dimensions. For a given material, the resistance is proportional to the cross-sectional area. For example, a copper wire has lower resistance than an otherwise-identical thin copper wire. Also, for a material, the resistance is proportional to the length, for example. The resistance R and conductance G of a conductor of uniform cross section, therefore, the resistivity and conductivity are proportionality constants, and therefore depend only on the material the wire is made of, not the geometry of the wire. Resistivity and conductivity are reciprocals, ρ =1 / σ, resistivity is a measure of the materials ability to oppose electric current. This formula is not exact, It assumes the current density is uniform in the conductor. However, this still provides a good approximation for long thin conductors such as wires. Another situation this formula is not exact for is with alternating current, then, the geometrical cross-section is different from the effective cross-section in which current actually flows, so the resistance is higher than expected. Similarly, if two conductors are each other carrying AC current, their resistances increase due to the proximity effect. Aside from the geometry of the wire, temperature also has a significant effect on the efficacy of conductors, temperature affects conductors in two main ways, the first is that materials may expand under the application of heat. The amount that the material will expand is governed by the expansion coefficient specific to the material. Such an expansion will change the geometry of the conductor and therefore its characteristic resistance, however, this effect is generally small, on the order of 10−6
19.
Superconductivity
–
It was discovered by Dutch physicist Heike Kamerlingh Onnes on April 8,1911, in Leiden. Like ferromagnetism and atomic spectral lines, superconductivity is a mechanical phenomenon. It is characterized by the Meissner effect, the ejection of magnetic field lines from the interior of the superconductor as it transitions into the superconducting state. The occurrence of the Meissner effect indicates that superconductivity cannot be simply as the idealization of perfect conductivity in classical physics. The electrical resistance of a metallic conductor decreases gradually as temperature is lowered, in ordinary conductors, such as copper or silver, this decrease is limited by impurities and other defects. Even near absolute zero, a sample of a normal conductor shows some resistance. In a superconductor, the resistance drops abruptly to zero when the material is cooled below its critical temperature, an electric current flowing through a loop of superconducting wire can persist indefinitely with no power source. In 1986, it was discovered that some cuprate-perovskite ceramic materials have a temperature above 90 K. Such a high temperature is theoretically impossible for a conventional superconductor. There are many criteria by which superconductors are classified, by theory of operation, It is conventional if it can be explained by the BCS theory or its derivatives, or unconventional, otherwise. By material, Superconductor material classes include chemical elements, alloys, ceramics, on the other hand, there is a class of properties that are independent of the underlying material. For instance, all superconductors have exactly zero resistivity to low applied currents when there is no magnetic field present or if the field does not exceed a critical value. The resistance of the sample is given by Ohms law as R = V / I, if the voltage is zero, this means that the resistance is zero. Superconductors are also able to maintain a current with no applied voltage whatsoever, experiments have demonstrated that currents in superconducting coils can persist for years without any measurable degradation. Experimental evidence points to a current lifetime of at least 100,000 years, theoretical estimates for the lifetime of a persistent current can exceed the estimated lifetime of the universe, depending on the wire geometry and the temperature. In a normal conductor, an electric current may be visualized as a fluid of electrons moving across an ionic lattice. As a result, the energy carried by the current is constantly being dissipated and this is the phenomenon of electrical resistance and Joule heating. The situation is different in a superconductor, in a conventional superconductor, the electronic fluid cannot be resolved into individual electrons
20.
Thermoelectric effect
–
The thermoelectric effect is the direct conversion of temperature differences to electric voltage and vice versa. A thermoelectric device creates voltage when there is a different temperature on each side, conversely, when a voltage is applied to it, it creates a temperature difference. At the atomic scale, a temperature gradient causes charge carriers in the material to diffuse from the hot side to the cold side. This effect can be used to generate electricity, measure temperature or change the temperature of objects, because the direction of heating and cooling is determined by the polarity of the applied voltage, thermoelectric devices can be used as temperature controllers. The term thermoelectric effect encompasses three separately identified effects, the Seebeck effect, Peltier effect, and Thomson effect, textbooks may refer to it as the Peltier–Seebeck effect. This separation derives from the independent discoveries of French physicist Jean Charles Athanase Peltier, Joule heating, the heat that is generated whenever a current is passed through a resistive material, is related, though it is not generally termed as thermoelectric effect. The Peltier–Seebeck and Thomson effects are reversible, whereas Joule heating is not. The Seebeck effect is the conversion of heat directly into electricity at the junction of different types of wire, Seebeck did not recognize there was an electric current involved, so he called the phenomenon thermomagnetic effect. Danish physicist Hans Christian Ørsted rectified the oversight and coined the term thermoelectricity, the Seebeck effect is a classic example of an electromotive force and leads to measurable currents or voltages in the same way as any other emf. The Seebeck coefficients generally vary as function of temperature, and depend strongly on the composition of the conductor, for ordinary materials at room temperature, the Seebeck coefficient may range in value from −100 μV/K to +1,000 μV/K. If the system reaches a state where J =0, then the voltage gradient is given simply by the emf. It is used commercially to identify metal alloys, thermocouples in series form a thermopile. Thermoelectric generators are used for creating power from heat differentials, when a current is made to flow through a junction between two conductors, A and B, heat may be generated or removed at the junction. The Peltier heat generated at the junction per unit time, Q ˙, is equal to Q ˙ = I where Π A is the Peltier coefficient of conductor A, and I is the electric current. The total heat generated is not determined by the Peltier effect alone, as it may also be influenced by Joule heating, the Peltier coefficients represent how much heat is carried per unit charge. Since charge current must be continuous across a junction, the heat flow will develop a discontinuity if Π A and Π B are different. The close relationship between Peltier and Seebeck effects can be seen in the connection between their coefficients, Π = T S. A typical Peltier heat pump device involves multiple junctions in series, some of the junctions lose heat due to the Peltier effect, while others gain heat
21.
Piezoelectricity
–
Piezoelectricity /piˌeɪzoʊˌilɛkˈtrɪsɪti/ is the electric charge that accumulates in certain solid materials in response to applied mechanical stress. The word piezoelectricity means electricity resulting from pressure and it is derived from the Greek piezō or piezein, which means to squeeze or press, and ēlektron, which means amber, an ancient source of electric charge. Piezoelectricity was discovered in 1880 by French physicists Jacques and Pierre Curie, the piezoelectric effect is understood as the linear electromechanical interaction between the mechanical and the electrical state in crystalline materials with no inversion symmetry. The piezoelectric effect is a process in that materials exhibiting the direct piezoelectric effect also exhibit the reverse piezoelectric effect. For example, lead zirconate titanate crystals will generate measurable piezoelectricity when their structure is deformed by about 0. 1% of the original dimension. Conversely, those same crystals will change about 0. 1% of their static dimension when an electric field is applied to the material. The inverse piezoelectric effect is used in the production of sound waves. The pyroelectric effect, by which a material generates a potential in response to a temperature change, was studied by Carl Linnaeus. Drawing on this knowledge, both René Just Haüy and Antoine César Becquerel posited a relationship between stress and electric charge, however, experiments by both proved inconclusive. The first demonstration of the piezoelectric effect was in 1880 by the brothers Pierre Curie. Quartz and Rochelle salt exhibited the most piezoelectricity, the Curies, however, did not predict the converse piezoelectric effect. The converse effect was mathematically deduced from fundamental principles by Gabriel Lippmann in 1881. For the next few decades, piezoelectricity remained something of a laboratory curiosity, more work was done to explore and define the crystal structures that exhibited piezoelectricity. The first practical application for piezoelectric devices was sonar, first developed during World War I, in France in 1917, Paul Langevin and his coworkers developed an ultrasonic submarine detector. The detector consisted of a transducer, made of quartz crystals carefully glued between two steel plates, and a hydrophone to detect the returned echo. The use of piezoelectricity in sonar, and the success of that project, over the next few decades, new piezoelectric materials and new applications for those materials were explored and developed. Piezoelectric devices found homes in many fields, ceramic phonograph cartridges simplified player design, were cheap and accurate, and made record players cheaper to maintain and easier to build. The development of the ultrasonic transducer allowed for easy measurement of viscosity and elasticity in fluids and solids, ultrasonic time-domain reflectometers could find flaws inside cast metal and stone objects, improving structural safety
22.
Ferroelectricity
–
Ferroelectricity is a property of certain materials that have a spontaneous electric polarization that can be reversed by the application of an external electric field. The term is used in analogy to ferromagnetism, in which a material exhibits a permanent magnetic moment, ferromagnetism was already known when ferroelectricity was discovered in 1920 in Rochelle salt by Valasek. Thus, the prefix ferro, meaning iron, was used to describe the property despite the fact that most ferroelectric materials do not contain iron. When most materials are polarized, the polarization induced, P, is almost exactly proportional to the external electric field E. Some materials, known as paraelectric materials, show a more enhanced nonlinear polarization, the electric permittivity, corresponding to the slope of the polarization curve, is not constant as in dielectrics but is a function of the external electric field. In addition to being nonlinear, ferroelectric materials demonstrate a spontaneous nonzero polarization even when the applied field E is zero and they are called ferroelectrics by analogy to ferromagnetic materials, which have spontaneous magnetization and exhibit similar hysteresis loops. Many ferroelectrics lose their piezoelectric properties above Tc completely, because their paraelectric phase has centrosymmetric crystallographic structure, the nonlinear nature of ferroelectric materials can be used to make capacitors with tunable capacitance. Typically, a ferroelectric capacitor simply consists of a pair of electrodes sandwiching a layer of ferroelectric material, the permittivity of ferroelectrics is not only tunable but commonly also very high in absolute value, especially when close to the phase transition temperature. Because of this, ferroelectric capacitors are small in size compared to dielectric capacitors of similar capacitance. In these applications thin films of materials are typically used. However, when using thin films a great deal of attention needs to be paid to the interfaces, electrodes, ferroelectric materials are required by symmetry considerations to be also piezoelectric and pyroelectric. The combined properties of memory, piezoelectricity, and pyroelectricity make ferroelectric capacitors very useful, ferroelectric capacitors are used in medical ultrasound machines, high quality infrared cameras, fire sensors, sonar, vibration sensors, and even fuel injectors on diesel engines. Another idea of recent interest is the tunnel junction in which a contact made up by nanometer-thick ferroelectric film placed between metal electrodes. The thickness of the layer is small enough to allow tunneling of electrons. The piezoelectric and interface effects as well as the depolarization field may lead to a giant electroresistance switching effect, the internal electric dipoles of a ferroelectric material are coupled to the material lattice so anything that changes the lattice will change the strength of the dipoles. The change in the spontaneous polarization results in a change in the surface charge and this can cause current flow in the case of a ferroelectric capacitor even without the presence of an external voltage across the capacitor. Two stimuli that change the lattice dimensions of a material are force. The generation of a charge in response to the application of an external stress to a material is called piezoelectricity
23.
Topological insulator
–
However, the conducting surface is not the unique character of topological insulators, since the ordinary band insulators can also support conductive surface states. What is special is that the states of topological insulators are symmetry protected by particle number conservation. In the bulk of a topological insulator, the electronic band structure resembles an ordinary band insulator. On the surface of a topological insulator there are states that fall within the bulk energy gap. Carriers in these states have their spin locked at a right-angle to their momentum. At a given energy the only other available electronic states have different spin, so the U-turn scattering is strongly suppressed, non-interacting topological insulators are characterized by an index similar to the genus in topology. The protected conducting states in the surface are required by time-reversal symmetry, time-reversal symmetry protected edge states were predicted in 1987 to occur in quantum wells of mercury telluride sandwiched between cadmium telluride and were observed in 2007. In 2007, they were predicted to occur in three-dimensional bulk solids of binary compounds involving bismuth, a 3D strong topological insulator exists which cannot be reduced to multiple copies of the quantum spin Hall state. The first experimentally realized 3D topological insulator state was discovered in bismuth-antimony, shortly thereafter symmetry protected surface states were also observed in pure antimony, bismuth selenide, bismuth telluride and antimony telluride using ARPES. Many semiconductors within the family of Heusler materials are now believed to exhibit topological surface states. In some of these materials the Fermi level actually falls in either the conduction or valence bands due to naturally occurring defects, the surface states of a 3D topological insulator is a new type of 2DEG where the electrons spin is locked to its linear momentum. Fully bulk insulating or intrinsic 3D topological insulator states exist in Bi-based materials, in 2014 it was shown that magnetic components, like the ones in computer memory, can be manipulated by topological insulators. The non-trivialness of topological insulators is encoded in the existence of a gas of helical Dirac fermions, helical Dirac fermions, which behave like massless relativistic particles, have been observed in 3D topological insulators. The Z2 topological invariants cannot be measured using traditional methods, such as spin Hall conductance. An experimental method to measure Z2 topological invariants was demonstrated which provide a measure of the Z2 topological order, hasan, M. Zahid, Kane, Charles L. Topological Insulators. Kane, Charles L. Moore, Joel E. Topological Insulators, Kane, Charles L. Topological Insulator, An Insulator with a Twist. Witze, A. Topological Insulators, Physics On the Edge, brumfiel, G. Topological insulators, Star material, Nature News. Topological Insulators, by Joel E. Moore, IEEE Spectrum, July 2011
24.
Quantum Hall effect
–
The prefactor, ν is known as the filling factor, and can take on either integer or fractional values. The quantum Hall effect is referred to as the integer or fractional quantum Hall effect depending on whether ν is an integer or fraction, the striking feature of the integer quantum Hall effect is the persistence of the quantization as the electron density is varied. The fractional quantum Hall effect is more complicated, as its existence relies fundamentally on electron–electron interactions, although the microscopic origins of the fractional quantum Hall effect are unknown, there are several phenomenological approaches that provide accurate approximations. For example, the effect can be thought of as an integer quantum Hall effect, not of electrons, in 1988, it was proposed that there was quantum Hall effect without Landau levels. This quantum Hall effect is referred to as the quantum anomalous Hall effect, there is also a new concept of the quantum spin Hall effect which is an analogue of the quantum Hall effect, where spin currents flow instead of charge currents. The quantization of the Hall conductance has the important property of being exceedingly precise, actual measurements of the Hall conductance have been found to be integer or fractional multiples of e2/h to nearly one part in a billion. This phenomenon, referred to as exact quantization, has shown to be a subtle manifestation of the principle of gauge invariance. It has allowed for the definition of a new standard for electrical resistance. This is named after Klaus von Klitzing, the discoverer of exact quantization, since 1990, a fixed conventional value RK-90 is used in resistance calibrations worldwide. The quantum Hall effect also provides an extremely precise independent determination of the structure constant. Several researchers subsequently observed the effect in experiments carried out on the layer of MOSFETs. For this finding, von Klitzing was awarded the 1985 Nobel Prize in Physics, the link between exact quantization and gauge invariance was subsequently found by Robert Laughlin, who connected the quantized conductivity to the quantized charge transport in Thouless charge pump. Most integer quantum Hall experiments are now performed on gallium arsenide heterostructures, in 2007, the integer quantum Hall effect was reported in graphene at temperatures as high as room temperature, and in the oxide ZnO-MgxZn1−xO. In two dimensions, when electrons are subjected to a magnetic field they follow circular cyclotron orbits. When the system is treated quantum mechanically, these orbits are quantized, the energy levels of these quantized orbitals take on discrete values, E n = ℏ ω c, where ωc = eB/m is the cyclotron frequency. For strong magnetic fields, each Landau level is highly degenerate, the integers that appear in the Hall effect are examples of topological quantum numbers. They are known in mathematics as the first Chern numbers and are related to Berrys phase. A striking model of much interest in this context is the Azbel-Harper-Hofstadter model whose quantum phase diagram is the Hofstadter butterfly shown in the figure, the vertical axis is the strength of the magnetic field and the horizontal axis is the chemical potential, which fixes the electron density
25.
Spin Hall effect
–
The Spin Hall Effect is a transport phenomenon predicted by Russian physicists M. I. It consists of the appearance of spin accumulation on the surfaces of an electric current-carrying sample. In a cylindrical wire, the current-induced surface spins will wind around the wire, when the current direction is reversed, the directions of spin orientation is also reversed. The Spin Hall Effect is a phenomenon consisting of the appearance of spin accumulation on the lateral surfaces of a sample carrying electric current. The opposing surface boundaries will have spins of opposite sign and it is analogous to the classical Hall effect, where charges of opposite sign appear on the opposing lateral surfaces in an electric-current carrying sample in a magnetic field. In the case of the classical Hall effect the charge build up at the boundaries is in compensation for the Lorentz force acting on the carriers in the sample due to the magnetic field. No magnetic field is needed for the SHE which is a purely spin-based phenomenon, the SHE belongs to the same family as the anomalous Hall effect, known for a long time in ferromagnets, which also originates from spin-orbit interaction. The term Spin Hall Effect was introduced by Jorge Hirsch in 1999, unaware of the work of Dyakonov and Perel, Hirsch used subtle physical reasoning based on the anomalous Hall effect to predict both the SHE and the inverse SHE. Averkiev and Dyakonov had earlier predicted the SHE, and it had been observed, experimentally, the Spin Hall Effect was observed in semiconductors more than 30 years after the original prediction. No magnetic field is needed for SHE, the SHE can be monitored by optical means. The spin accumulation induces circular polarization of the light, as well as the Faraday polarization rotation of the transmitted light. Observing the polarization of emitted light allows the SHE to be observed and this can be measured as a charge imbalance at the edges of the sample. It was first observed in 1984, more recently, the existence of both direct and inverse effects was demonstrated not only in semiconductors, but also in metals. The SHE can be used to manipulate electron spins electrically, for example, in combination with the electric stirring effect, the SHE leads to spin polarization in a localized conducting region
26.
Kondo effect
–
In physics, the Kondo effect describes the scattering of conduction electrons in a metal due to magnetic impurities, resulting in a characteristic change in electrical resistivity with temperature. Jun Kondo derived the term of the logarithmic dependence. Later calculations refined this result to produce a finite resistivity but retained the feature of a minimum at a non-zero temperature. One defines the Kondo temperature as the energy scale limiting the validity of the Kondo results, the Anderson impurity model and accompanying renormalization theory were an important contribution to understanding the underlying physics of the problem. The Kondo effect can be considered as an example of freedom, i. e. a situation where the coupling becomes non-perturbatively strong at low temperatures. In the Kondo problem, the coupling refers to the interaction between the localized magnetic impurities and the itinerant electrons, in a number of instances they actually are superconductors. More recently, it is believed that a manifestation of the Kondo effect is necessary for understanding the unusual metallic delta-phase of plutonium, more recently the Kondo effect has been observed in quantum dot systems. This is completely analogous to the traditional case of a magnetic impurity in a metal. Kondo Effect -40 Years after the Discovery - special issue of the Journal of the Physical Society of Japan The Kondo Problem to Heavy Fermions - Monograph on the Kondo effect by A. C, nature article exploring the links of the Kondo effect and plutonium
27.
Diamagnetism
–
Diamagnetic materials are repelled by a magnetic field, an applied magnetic field creates an induced magnetic field in them in the opposite direction, causing a repulsive force. In contrast, paramagnetic and ferromagnetic materials are attracted by a magnetic field, diamagnetism is a quantum mechanical effect that occurs in all materials, when it is the only contribution to the magnetism the material is called diamagnetic. In paramagnetic and ferromagnetic substances the weak force is overcome by the attractive force of magnetic dipoles in the material. The magnetic permeability of diamagnetic materials is less than μ0, the permeability of vacuum, diamagnetism was first discovered when Sebald Justinus Brugmans observed in 1778 that bismuth and antimony were repelled by magnetic fields. In 1845, Michael Faraday demonstrated that it was a property of matter and he adopted the term diamagnetism after it was suggested to him by William Whewell. Diamagnetism, to a greater or lesser degree, is a property of all materials, for materials that show some other form of magnetism, the diamagnetic contribution becomes negligible. Substances that mostly display diamagnetic behaviour are termed diamagnetic materials, or diamagnets, the magnetic susceptibility values of various molecular fragments are called Pascals constants. This means that diamagnetic materials are repelled by magnetic fields, however, since diamagnetism is such a weak property, its effects are not observable in everyday life. For example, the susceptibility of diamagnets such as water is χv = −9. 05×10−6. The most strongly diamagnetic material is bismuth, χv = −1. 66×10−4, nevertheless, these values are orders of magnitude smaller than the magnetism exhibited by paramagnets and ferromagnets. Note that because χv is derived from the ratio of the magnetic field to the applied field. All conductors exhibit an effective diamagnetism when they experience a magnetic field. The Lorentz force on electrons causes them to circulate around forming eddy currents, the eddy currents then produce an induced magnetic field opposite the applied field, resisting the conductors motion. Superconductors may be considered perfect diamagnets, because they expel all fields due to the Meissner effect, however this effect is not due to eddy currents, as in ordinary diamagnetic materials. If a powerful magnet is covered with a layer of water then the field of the magnet significantly repels the water and this causes a slight dimple in the waters surface that may be seen by its reflection. Diamagnets may be levitated in stable equilibrium in a magnetic field, Earnshaws theorem seems to preclude the possibility of static magnetic levitation. However, Earnshaws theorem applies only to objects with positive susceptibilities and these are attracted to field maxima, which do not exist in free space. Diamagnets are attracted to field minima, and there can be a minimum in free space
28.
Superdiamagnetism
–
Superdiamagnetism is a phenomenon occurring in certain materials at low temperatures, characterised by the complete absence of magnetic permeability and the exclusion of the interior magnetic field. Superdiamagnetism established that the superconductivity of a material was a stage of phase transition, superconducting magnetic levitation is due to superdiamagnetism, which repels a permanent magnet which approaches the superconductor, and flux pinning, which prevents the magnet floating away. Superdiamagnetism is a feature of superconductivity and these screening currents are generated whenever a superconducting material is brought inside a magnetic field. This can be understood by the fact that a superconductor has zero electrical resistance, so eddy currents, induced by the motion of the material inside a magnetic field. Fritz, at the Royal Society in 1935, stated that the state would be described by a single wave function. Screening currents also appear in a situation wherein an initially normal, as soon as the metal is cooled below the appropriate transition temperature, it becomes superconducting. This expulsion of magnetic field upon the cooling of the metal cannot be explained any longer by merely assuming zero resistance and is called the Meissner effect, superfluidity Timeline of low-temperature technology Shachtman, Tom, Absolute Zero, And the Conquest of Cold
29.
Paramagnetism
–
In contrast with this behavior, diamagnetic materials are repelled by magnetic fields and form induced magnetic fields in the direction opposite to that of the applied magnetic field. Paramagnetic materials include most chemical elements and some compounds, they have a magnetic permeability greater than or equal to 1. The magnetic moment induced by the field is linear in the field strength. It typically requires a sensitive balance to detect the effect. Paramagnetic materials have a small, positive susceptibility to magnetic fields and these materials are slightly attracted by a magnetic field and the material does not retain the magnetic properties when the external field is removed. Paramagnetic properties are due to the presence of unpaired electrons. Paramagnetic materials include magnesium, molybdenum, lithium, and tantalum, unlike ferromagnets, paramagnets do not retain any magnetization in the absence of an externally applied magnetic field because thermal motion randomizes the spin orientations. Thus the total magnetization drops to zero when the field is removed. Even in the presence of the field there is only a small induced magnetization because only a fraction of the spins will be oriented by the field. This fraction is proportional to the strength and this explains the linear dependency. Constituent atoms or molecules of paramagnetic materials have permanent magnetic moments, the permanent moment generally is due to the spin of unpaired electrons in atomic or molecular electron orbitals. In pure paramagnetism, the dipoles do not interact with one another and are oriented in the absence of an external field due to thermal agitation. When a magnetic field is applied, the dipoles will tend to align with the applied field, however, the true origins of the alignment can only be understood via the quantum-mechanical properties of spin and angular momentum. Paramagnetic behavior can also be observed in materials that are above their Curie temperature. At these temperatures, the thermal energy simply overcomes the interaction energy between the spins. In conductive materials the electrons are delocalized, that is, they travel through the more or less as free electrons. Conductivity can be understood in a band structure picture as arising from the filling of energy bands. In an ordinary nonmagnetic conductor the band is identical for both spin-up and spin-down electrons
30.
Superparamagnetism
–
Superparamagnetism is a form of magnetism, which appears in small ferromagnetic or ferrimagnetic nanoparticles. In sufficiently small nanoparticles, magnetization can randomly flip direction under the influence of temperature, the typical time between two flips is called the Néel relaxation time. In this state, a magnetic field is able to magnetize the nanoparticles. However, their magnetic susceptibility is much larger than that of paramagnets, normally, any ferromagnetic or ferrimagnetic material undergoes a transition to a paramagnetic state above its Curie temperature. Superparamagnetism is different from this standard transition since it occurs below the Curie temperature of the material, superparamagnetism occurs in nanoparticles which are single-domain, i. e. composed of a single magnetic domain. This is possible when their diameter is below 3–50 nm, depending on the materials, in this condition, it is considered that the magnetization of the nanoparticles is a single giant magnetic moment, sum of all the individual magnetic moments carried by the atoms of the nanoparticle. Those in the field of superparamagnetism call this “macro-spin approximation”, because of the nanoparticle’s magnetic anisotropy, the magnetic moment has usually only two stable orientations antiparallel to each other, separated by an energy barrier. The stable orientations define the nanoparticle’s so called “easy axis”, at finite temperature, there is a finite probability for the magnetization to flip and reverse its direction. τ0 is a length of time, characteristic of the material, called the time or attempt period. K is the magnetic anisotropy energy density and V its volume. KV is therefore the energy associated with the magnetization moving from its initial easy axis direction, through a “hard plane”. This length of time can be anywhere from a few nanoseconds to years or much longer, let us imagine that the magnetization of a single superparamagnetic nanoparticle is measured and let us define τ m as the measurement time. If τ m ≫ τ N, the magnetization will flip several times during the measurement. If τ m ≪ τ N, the magnetization will not flip during the measurement, in the former case, the nanoparticle will appear to be in the superparamagnetic state whereas in the latter case it will appear to be “blocked” in its initial state. The state of the nanoparticle depends on the measurement time, a transition between superparamagnetism and blocked state occurs when τ m = τ N. In several experiments, the measurement time is kept constant but the temperature is varied, when an external magnetic field is applied to an assembly of superparamagnetic nanoparticles, their magnetic moments tend to align along the applied field, leading to a net magnetization. The magnetization curve of the assembly, i. e. the magnetization as a function of the field, is a reversible S-shaped increasing function. The later susceptibility is also valid for all temperatures T > T B if the easy axes of the nanoparticles are randomly oriented and it can be seen from these equations that large nanoparticles have a larger µ and so a larger susceptibility
31.
Ferromagnetism
–
Not to be confused with Ferrimagnetism, for an overview see Magnetism. Ferromagnetism is the mechanism by which certain materials form permanent magnets. In physics, several different types of magnetism are distinguished, an everyday example of ferromagnetism is a refrigerator magnet used to hold notes on a refrigerator door. The attraction between a magnet and ferromagnetic material is the quality of magnetism first apparent to the ancient world, permanent magnets are either ferromagnetic or ferrimagnetic, as are the materials that are noticeably attracted to them. Only a few substances are ferromagnetic, the common ones are iron, nickel, cobalt and most of their alloys, some compounds of rare earth metals, and a few naturally occurring minerals, including some varieties of lodestone. Historically, the term ferromagnetism was used for any material that could exhibit spontaneous magnetization and this general definition is still in common use. In particular, a material is ferromagnetic in this sense only if all of its magnetic ions add a positive contribution to the net magnetization. If some of the magnetic ions subtract from the net magnetization, if the moments of the aligned and anti-aligned ions balance completely so as to have zero net magnetization, despite the magnetic ordering, then it is an antiferromagnet. These alignment effects only occur at temperatures below a critical temperature. Among the first investigations of ferromagnetism are the works of Aleksandr Stoletov on measurement of the magnetic permeability of ferromagnetics. The table on the right lists a selection of ferromagnetic and ferrimagnetic compounds, ferromagnetism is a property not just of the chemical make-up of a material, but of its crystalline structure and microstructure. There are ferromagnetic metal alloys whose constituents are not themselves ferromagnetic, called Heusler alloys, conversely there are non-magnetic alloys, such as types of stainless steel, composed almost exclusively of ferromagnetic metals. Amorphous ferromagnetic metallic alloys can be made by rapid quenching of a liquid alloy. These have the advantage that their properties are isotropic, this results in low coercivity, low hysteresis loss, high permeability. One such typical material is a transition metal-metalloid alloy, made from about 80% transition metal, a relatively new class of exceptionally strong ferromagnetic materials are the rare-earth magnets. They contain lanthanide elements that are known for their ability to carry large magnetic moments in well-localized f-orbitals, a number of actinide compounds are ferromagnets at room temperature or exhibit ferromagnetism upon cooling. PuP is a paramagnet with cubic symmetry at room temperature, in its ferromagnetic state, PuPs easy axis is in the <100> direction. In NpFe2 the easy axis is <111>, above TC ≈500 K NpFe2 is also paramagnetic and cubic
32.
Antiferromagnetism
–
This is, like ferromagnetism and ferrimagnetism, a manifestation of ordered magnetism. Generally, antiferromagnetic order may exist at low temperatures, vanishing at and above a certain temperature. Above the Néel temperature, the material is typically paramagnetic, when no external field is applied, the antiferromagnetic structure corresponds to a vanishing total magnetization. Although the net magnetization should be zero at a temperature of absolute zero, the magnetic susceptibility of an antiferromagnetic material typically shows a maximum at the Néel temperature. In contrast, at the transition between the ferromagnetic to the paramagnetic phases the susceptibility will diverge, in the antiferromagnetic case, a divergence is observed in the staggered susceptibility. Various microscopic interactions between the magnetic moments or spins may lead to antiferromagnetic structures, in the simplest case, one may consider an Ising model on a bipartite lattice, e. g. the simple cubic lattice, with couplings between spins at nearest neighbor sites. Depending on the sign of that interaction, ferromagnetic or antiferromagnetic order will result, geometrical frustration or competing ferro- and antiferromagnetic interactions may lead to different and, perhaps, more complicated magnetic structures. Antiferromagnetic materials occur commonly among transition metal compounds, especially oxides, examples include hematite, metals such as chromium, alloys such as iron manganese, and oxides such as nickel oxide. There are also numerous examples among high nuclearity metal clusters, organic molecules can also exhibit antiferromagnetic coupling under rare circumstances, as seen in radicals such as 5-dehydro-m-xylylene. Unlike ferromagnetism, anti-ferromagnetic interactions can lead to multiple optimal states, in one dimension, the anti-ferromagnetic ground state is an alternating series of spins, up, down, up, down, etc. Yet in two dimensions, multiple ground states can occur, consider an equilateral triangle with three spins, one on each vertex. If each spin can take on two values, there are 23 =8 possible states of the system, six of which are ground states. The two situations which are not ground states are all three spins are up or are all down. In any of the six states, there will be two favorable interactions and one unfavorable one. This illustrates frustration, the inability of the system to find a ground state. This type of behavior has been found in minerals that have a crystal stacking structure such as a Kagome lattice or hexagonal lattice. Synthetic antiferromagnets are artificial antiferromagnets consisting of two or more thin ferromagnetic layers separated by a nonmagnetic layer, due to dipole coupling of the ferromagnetic layers results in antiparallel alignment of the magnetization of the ferromagnets. Antiferromagnetism plays a role in giant magnetoresistance, as had been discovered in 1988 by the Nobel prize winners Albert Fert
33.
Spin glass
–
A spin glass is a disordered magnet, where the magnetic spin of the component atoms are not aligned in a regular pattern. The term glass comes from an analogy between the disorder in a spin glass and the positional disorder of a conventional, chemical glass. In window glass or any amorphous solid the atomic structure is highly irregular, in contrast. In ferromagnetic solid, magnetic spins all align in the same direction, the individual atomic bonds in a spin glass are a mixture of roughly equal numbers of ferromagnetic bonds and antiferromagnetic bonds. They may also create situations where more than one geometric arrangement of atoms is stable, Spin glasses and the complex internal structures that arise within them are termed metastable because they are stuck in stable configurations other than the lowest-energy configuration. It is the time dependence which distinguishes spin glasses from other magnetic systems, above the spin glass transition temperature, Tc, the spin glass exhibits typical magnetic behaviour. If a magnetic field is applied as the sample is cooled to the transition temperature, upon reaching Tc, the sample becomes a spin glass and further cooling results in little change in magnetization. This is referred to as the field-cooled magnetization, when the external magnetic field is removed, the magnetization of the spin glass falls rapidly to a lower value known as the remanent magnetization. Magnetization then decays slowly as it approaches zero and this decay is non-exponential and no simple function can fit the curve of magnetization versus time adequately. This slow decay is particular to spin glasses, Experimental measurements on the order of days have shown continual changes above the noise level of instrumentation. Paramagnetic materials differ from spin glasses by the fact that, after the magnetic field is removed. In each case the decay is rapid and exponential, a slow upward drift then occurs toward the field-cooled magnetization. In this model, we have spins arranged on a d -dimensional lattice with only nearest neighbor interactions similar to the Ising model and this model can be solved exactly for the critical temperatures and a glassy phase is observed to exist at low temperatures. The Hamiltonian for this system is given by, H = − ∑ ⟨ i j ⟩ J i j S i S j. A negative value of J i j denotes an antiferromagnetic type interaction between spins at points i and j, the sum runs over all nearest neighbor positions on a lattice, of any dimension. The variables J i j magnetic nature of the interactions are called bond or link variables. In order to determine the function for this system, one needs to average the free energy f = −1 β ln Z where Z = Tr S e. The distribution of values of J i j is taken to be a gaussian with a mean J0, the order parameter for the ferromagnetic to spin glass phase transition is therefore q, and that for paramagnetic to spin glass is again q
34.
Quasiparticle
–
This electron with a different mass is called an electron quasiparticle. In another example, the motion of electrons in the valence band of a semiconductor is the same as if the semiconductor instead contained positively charged quasiparticles called holes. Other quasiparticles or collective excitations include phonons, plasmons, and many others, thus, electrons and holes are typically called quasiparticles, while phonons and plasmons are typically called collective excitations. The quasiparticle concept is most important in condensed matter physics since it is one of the few ways of simplifying the quantum mechanical many-body problem. Solids are made of three kinds of particles, Electrons, protons, and neutrons. Quasiparticles are none of these, instead, they are an emergent phenomenon that occurs inside the solid, therefore, while it is quite possible to have a single particle floating in space, a quasiparticle can instead only exist inside the solid. Motion in a solid is extremely complicated, Each electron and proton is pushed and pulled by all the electrons and protons in the solid. It is these strong interactions that make it difficult to predict. In summary, quasiparticles are a tool for simplifying the description of solids. They are not real particles inside the solid, instead, saying A quasiparticle is present or A quasiparticle is moving is shorthand for saying A large number of electrons and nuclei are moving in a specific coordinated way. The principal motivation for quasiparticles is that it is almost impossible to describe every particle in a macroscopic system. For example, a grain of sand contains around 1017 nuclei and 1018 electrons. Each of these attracts or repels every other by Coulombs law, in quantum mechanics, a system is described by a wavefunction, which, if the particles are interacting, depends on the position of every particle in the system. So, each particle adds three independent variables to the wavefunction, one for each coordinate needed to describe the position of that particle. One simplifying factor is that the system as a whole, like any quantum system, has a ground state, in many contexts, only the low-lying excited states, with energy reasonably close to the ground state, are relevant. This occurs because of the Boltzmann distribution, which implies that very-high-energy thermal fluctuations are unlikely to occur at any given temperature, quasiparticles and collective excitations are a type of low-lying excited state. For example, a crystal at absolute zero is in the ground state, the single phonon is called an elementary excitation. More generally, low-lying excited states may contain any number of elementary excitations, when the material is characterized as having several elementary excitations, this statement presupposes that the different excitations can be combined together
35.
Phonon
–
In physics, a phonon is a collective excitation in a periodic, elastic arrangement of atoms or molecules in condensed matter, like solids and some liquids. Often designated a quasiparticle, it represents a state in the quantum mechanical quantization of the modes of vibrations of elastic structures of interacting particles. Phonons play a role in many of the physical properties of condensed matter, like thermal conductivity. The study of phonons is an important part of condensed matter physics, the concept of phonons was introduced in 1932 by Soviet physicist Igor Tamm. The name phonon comes from the Greek word φωνή, which translates to sound or voice because long-wavelength phonons give rise to sound, shorter-wavelength higher-frequency phonons are responsible for the majority of the thermal capacity of solids. A phonon is a quantum description of an elementary vibrational motion in which a lattice of atoms or molecules uniformly oscillates at a single frequency. In classical mechanics this designates a normal mode of vibration, normal modes are important because any arbitrary lattice vibration can be considered to be a superposition of these elementary vibration modes. While normal modes are wave-like phenomena in classical mechanics, phonons have particle-like properties too, the equations in this section do not use axioms of quantum mechanics but instead use relations for which there exists a direct correspondence in classical mechanics. For example, a regular, crystalline, lattice is composed of N particles. These particles may be atoms or molecules, N is a large number, say of the order of 1023, or on the order of Avogadros number for a typical sample of a solid. Since the lattice is rigid, the atoms must be exerting forces on one another to keep each atom near its equilibrium position. These forces may be Van der Waals forces, covalent bonds, electrostatic attractions, magnetic and gravitational forces are generally negligible. The forces between each pair of atoms may be characterized by an energy function V that depends on the distance of separation of the atoms. The potential energy of the lattice is the sum of all pairwise potential energies, ∑ i ≠ j V where ri is the position of the ith atom. It is difficult to solve this many-body problem explicitly in either classical or quantum mechanics, in order to simplify the task, two important approximations are usually imposed. First, the sum is only performed over neighboring atoms, although the electric forces in real solids extend to infinity, this approximation is still valid because the fields produced by distant atoms are effectively screened. Secondly, the potentials V are treated as harmonic potentials and this is permissible as long as the atoms remain close to their equilibrium positions. Formally, this is accomplished by Taylor expanding V about its value to quadratic order, giving V proportional to the displacement x2
36.
Exciton
–
An exciton is a bound state of an electron and an electron hole which are attracted to each other by the electrostatic Coulomb force. It is an electrically neutral quasiparticle that exists in insulators, semiconductors, the exciton is regarded as an elementary excitation of condensed matter that can transport energy without transporting net electric charge. An exciton can form when a photon is absorbed by a semiconductor and this excites an electron from the valence band into the conduction band. In turn, this leaves behind a positively charged electron hole, the electron in the conduction band is then effectively attracted to this localized hole by the repulsive Coulomb forces from large numbers of electrons surrounding the hole and excited electron. This attraction provides an energy balance. Consequently, the exciton has slightly less energy than the unbound electron, the wavefunction of the bound state is said to be hydrogenic, an exotic atom state akin to that of a hydrogen atom. However, the energy is much smaller and the particles size much larger than a hydrogen atom. This is because of both the screening of the Coulomb force by other electrons in the semiconductor, and the effective masses of the excited electron. The electron and hole may have parallel or anti-parallel spins. The spins are coupled by the interaction, giving rise to exciton fine structure. In periodic lattices, the properties of an exciton show momentum dependence, the concept of excitons was first proposed by Yakov Frenkel in 1931, when he described the excitation of atoms in a lattice of insulators. He proposed that this state would be able to travel in a particle-like fashion through the lattice without the net transfer of charge. Excitons may be treated in two limiting cases, depending on the properties of the material in question, molecular excitons may even be entirely located on the same molecule, as in fullerenes. This Frenkel exciton, named after Yakov Frenkel, has a binding energy on the order of 0.1 to 1 eV. Frenkel excitons are typically found in alkali halide crystals and in molecular crystals composed of aromatic molecules. In semiconductors, the constant is generally large. Consequently, electric field screening tends to reduce the Coulomb interaction between electrons and holes, the result is a Wannier exciton, which has a radius larger than the lattice spacing. Small effective mass of electrons that is typical of semiconductors also favors large exciton radii, as a result, the effect of the lattice potential can be incorporated into the effective masses of the electron and hole
37.
Plasmon
–
In physics, a plasmon is a quantum of plasma oscillation. Just as light consists of photons, the plasma oscillation consists of plasmons, the plasmon can be considered as a quasiparticle since it arises from the quantization of plasma oscillations, just like phonons are quantizations of mechanical vibrations. Thus, plasmons are collective oscillations of the electron gas density. For example, at frequencies, plasmons can couple with a photon to create another quasiparticle called a plasmon polariton. The plasmon was initially proposed in 1952 by David Pines and David Bohm and was shown to arise from a Hamiltonian for the long-range electron-electron correlations, since plasmons are the quantization of classical plasma oscillations, most of their properties can be derived directly from Maxwells equations. Plasmons can be described in the picture as an oscillation of free electron density with respect to the fixed positive ions in a metal. To visualize a plasma oscillation, imagine a cube of metal placed in an electric field pointing to the right. Electrons will move to the side until they cancel the field inside the metal. If the electric field is removed, the move to the right, repelled by each other. They oscillate back and forth at the plasma frequency until the energy is lost in some kind of resistance or damping, plasmons are a quantization of this kind of oscillation. Plasmons play a role in the optical properties of metals. Light of frequencies below the frequency is reflected by a material because the electrons in the material screen the electric field of the light. Light of frequencies above the frequency is transmitted by a material because the electrons in the material cannot respond fast enough to screen it. In most metals, the frequency is in the ultraviolet. Some metals, such as copper and gold, have electronic interband transitions in the range, whereby specific light energies are absorbed. It has been shown that the frequency may occur in the mid-infrared and near-infrared region when semiconductors are in the form of nanoparticles with heavy doping. Surface plasmons are those plasmons that are confined to surfaces and that interact strongly with light resulting in a polariton, the particular choice of materials can have a drastic effect on the degree of light confinement and propagation distance due to losses. Surface plasmons can also exist on other than flat surfaces, such as particles, or rectangular strips, v-grooves, cylinders
38.
Polariton
–
In physics, polaritons /pəˈlærᵻtɒnz, poʊ-/ are quasiparticles resulting from strong coupling of electromagnetic waves with an electric or magnetic dipole-carrying excitation. They are an expression of the quantum phenomenon known as level repulsion. Polaritons describe the crossing of the dispersion of light with any interacting resonance, the polariton is a bosonic quasiparticle, and should not be confused with the polaron, which is an electron plus an attached phonon cloud. Whenever the polariton picture is valid, the model of photons propagating freely in crystals is insufficient, a major feature of polaritons is a strong dependency of the propagation speed of light through the crystal on the frequency. For exciton-polaritons, rich experimental results on various aspects have been gained in copper oxide, oscillations in ionized gases were observed by Tonks and Langmuir in 1929. Polaritons were first considered theoretically by Tolpygo and they were termed light-excitons in Ukrainian and Russian scientific literature. That name was suggested by Pekar, but the term polariton, collective interactions were published by Pines and Bohm in 1952, and plasmons were described in silver by Fröhlich and Pelzer in 1955. Ritchie predicted surface plasmons in 1957, then Ritchie and Eldridge published experiments, otto first published on surface plasmon-polaritons in 1968. A polariton is the result of the mixing of a photon with an excitation of a material. Plexcitons result from coupling plasmons with excitons, atomic coherence Polariton laser Polariton superfluid Polaritonics Baker-Jarvis, J. The Interaction of Radio-Frequency Fields With Dielectric Materials at Macroscopic to Mesoscopic Scales, journal of Research of the National Institute of Standards and Technology. National Institute of Science and Technology, atomic Theory of Electromagnetic Interactions in Dense Materials. Hopfield, J. J. Theory of the Contribution of Excitons to the Complex Dielectric Constant of Crystals, youTube animation explaining what is polariton in a semiconductor micro-resonator
39.
Polaron
–
A polaron is a quasiparticle used in condensed matter physics to understand the interactions between electrons and atoms in a solid material. This lowers the electron mobility and increases the effective mass. Major theoretical work has focused on solving Fröhlich and Holstein Hamiltonians and this is still an active field of research to find exact numerical solutions to the case of one or two electrons in a large crystal lattice, and to study the case of many interacting electrons. Experimentally, polarons are important to the understanding of a variety of materials. The electron mobility in semiconductors can be decreased by the formation of polarons. Organic semiconductors are also sensitive to polaronic effects, which is relevant in the design of organic solar cells that effectively transport charge. The electron phonon interaction that forms Cooper pairs in low-Tc superconductors can also be modeled as a polaron and this has been suggested as a mechanism for Cooper pair formation in high-Tc superconductors. Polarons are also important for interpreting the optical conductivity of these types of materials, the polaron, a fermionic quasiparticle, should not be confused with the polariton, a bosonic quasiparticle analogous to a hybridized state between a photon and an optical phonon. The energy spectrum of an electron moving in a potential of rigid crystal lattice consists of allowed. An electron with energy inside an allowed band moves as a free electron but has a mass that differs from the electron mass in vacuum. However, a lattice is deformable and displacements of atoms from their equilibrium positions are described in terms of phonons. Electrons interact with these displacements, and this interaction is known as electron-phonon coupling, one of possible scenarios was proposed in the seminal 1933 paper by Lev Landau, which includes the production of a lattice defect such as an F-center and a trapping of the electron by this defect. A different scenario was proposed by Solomon Pekar that envisions dressing the electron with lattice deformation, such an electron with the accompanying deformation moves freely across the crystal, but with increased effective mass. Pekar coined for this charge carrier the term polaron, Pekar formed the basis of polaron theory. A charge placed in a medium will be screened. Dielectric theory describes the phenomenon by the induction of a polarization around the charge carrier, the induced polarization will follow the charge carrier when it is moving through the medium. The carrier together with the polarization is considered as one entity. A conduction electron in a crystal or a polar semiconductor is the prototype of a polaron
40.
Magnon
–
A magnon is a quasiparticle, a collective excitation of the electrons spin structure in a crystal lattice. In the equivalent wave picture of quantum mechanics, a magnon can be viewed as a spin wave. Magnons carry a fixed amount of energy and lattice momentum, and are spin-1, the concept of a magnon was introduced in 1930 by Felix Bloch in order to explain the reduction of the spontaneous magnetization in a ferromagnet. At absolute zero temperature, a Heisenberg ferromagnet reaches the state of lowest energy, as the temperature increases, more and more spins deviate randomly from the alignment, increasing the internal energy and reducing the net magnetization. Each magnon reduces the total spin along the direction of magnetization by one unit of ℏ and the magnetization by γ ℏ, where γ is the gyromagnetic ratio. This leads to Blochs law for the dependence of spontaneous magnetization, M = M0 where T c is the critical temperature. The quantitative theory of magnons, quantized spin waves, was developed further by Theodore Holstein, Henry Primakoff, using the second quantization formalism they showed that magnons behave as weakly interacting quasiparticles obeying Bose–Einstein statistics. A comprehensive treatment can be found in the state textbook by Charles Kittel or the early review article by Van Kranendonk. Direct experimental detection of magnons by inelastic neutron scattering in ferrite was achieved in 1957 by Bertram Brockhouse, since then magnons have been detected in ferromagnets, ferrimagnets, and antiferromagnets. The fact that magnons obey the Bose–Einstein statistics was confirmed by the scattering experiments done during the 1960s through the 1980s. Classical theory predicts equal intensity of Stokes and anti-Stokes lines, Bose–Einstein condensation of magnons was proven in an antiferromagnet at low temperatures by Nikuni et al. and in a ferrimagnet by Demokritov et al. at room temperature. Recently Uchida et al. reported the generation of spin currents by surface plasmon resonance, paramagnons are magnons in magnetic materials which are in their high temperature, disordered phase. For low enough temperatures, the local magnetic moments in ferromagnetic or anti-ferromagnetic compounds will become ordered. Small oscillations of the moments around their natural direction will propagate as waves, at temperatures higher than the critical temperature, long range order is lost, but spins will still align locally in patches, allowing for spin waves to propagate for short distances. These waves are known as a paramagnon, and undergo diffusive transport, magnon behavior can be studied with a variety of scattering techniques. Magnons behave as a Bose gas with no chemical potential, microwave pumping can be used to excite spin waves and create additional non-equilibrium magnons which thermalize into phonons. At a critical density, a condensate is formed, which appears as the emission of monochromatic microwaves and this microwave source can be tuned with an applied magnetic field. Kittel, Introduction to Solid State Physics, 7th edition, Bloch, F. Zur Theorie des Ferromagnetismus
41.
Amorphous solid
–
In condensed matter physics and materials science, an amorphous or non-crystalline solid is a solid that lacks the long-range order that is characteristic of a crystal. In some older books, the term has been used synonymously with glass, nowadays, glassy solid or amorphous solid is considered to be the overarching concept, and glass the more special case, A glass is an amorphous solid that exhibits a glass transition. Other types of solids include gels, thin films. Amorphous materials have a structure made of interconnected structural blocks. Even amorphous materials have some shortrange order at the length scale due to the nature of chemical bonding. Furthermore, in small crystals a large fraction of the atoms are the crystal, relaxation of the surface and interfacial effects distort the atomic positions. Amorphous phases are important constituents of thin films, which are layers of a few nm to some tens of µm thickness deposited upon a substrate. For higher values, the diffusion of deposited atomic species would allow for the formation of crystallites with long range atomic order. Regarding their applications, amorphous metallic layers played an important role in the discussion of a suspected superconductivity in amorphous metals, today, optical coatings made from TiO2, SiO2, Ta2O5 etc. and combinations of them in most cases consist of amorphous phases of these compounds. Much research is carried out into thin films as a gas separating membrane layer. Also, hydrogenated amorphous silicon, a-Si, H in short, is of significance for thin film solar cells. In case of a-Si, H the missing long-range order between silicon atoms is partly induced by the presence by hydrogen in the percent range, the occurrence of amorphous phases turned out as a phenomenon of particular interest for studying thin film growth. Remarkably, the growth of polycrystalline films is used and preceded by an initial amorphous layer. The most investigated example is represented by thin multicrystalline silicon films, an initial amorphous layer was observed in many studies. The phenomenon has been interpreted in the framework of Ostwalds rule of stages that predicts the formation of phases to proceed with increasing condensation time towards increasing stability. Experimental studies of the phenomenon require a clearly defined state of the substrate surface, the Physics of Structurally Disordered Matter, An Introduction. Amorphous Solids and the Liquid State
42.
Colloid
–
A colloid, in chemistry, is a mixture in which one substance of microscopically dispersed insoluble particles is suspended throughout another substance. Sometimes the dispersed substance alone is called the colloid, the colloidal suspension refers unambiguously to the overall mixture. Unlike a solution, whose solute and solvent constitute only one phase, a colloid has a dispersed phase, to qualify as a colloid, the mixture must be one that does not settle or would take a very long time to settle appreciably. The dispersed-phase particles have a diameter between approximately 1 and 1000 nanometers, such particles are normally easily visible in an optical microscope, although at the smaller size range, an ultramicroscope or an electron microscope may be required. Homogeneous mixtures with a phase in this size range may be called colloidal aerosols, colloidal emulsions, colloidal foams, colloidal dispersions. The dispersed-phase particles or droplets are affected largely by the surface chemistry present in the colloid, some colloids are translucent because of the Tyndall effect, which is the scattering of light by particles in the colloid. Other colloids may be opaque or have a slight color, Colloidal suspensions are the subject of interface and colloid science. This field of study was introduced in 1861 by Scottish scientist Thomas Graham, because of the size exclusion, the colloidal particles are unable to pass through the pores of an ultrafiltration membrane with a size smaller than their own dimension. The smaller the size of the pore of the ultrafiltration membrane, the measured value of the concentration of a truly dissolved species will thus depend on the experimental conditions applied to separate it from the colloidal particles also dispersed in the liquid. This is particularly important for solubility studies of readily hydrolyzed species such as Al, Eu, Am, Cm, the colloid particles are attracted toward water. They are also called reversible sols, hydrophobic colloids, These are opposite in nature to hydrophilic colloids. The colloid particles are repelled by water and they are also called irreversible sols. In some cases, a colloid suspension can be considered a homogeneous mixture and this is because the distinction between dissolved and particulate matter can be sometimes a matter of approach, which affects whether or not it is homogeneous or heterogeneous. The following forces play an important role in the interaction of particles, Excluded volume repulsion. Electrostatic interaction, Colloidal particles often carry a charge and therefore attract or repel each other. The charge of both the continuous and the phase, as well as the mobility of the phases are factors affecting this interaction. Van der Waals forces, This is due to interaction between two dipoles that are permanent or induced. Even if the particles do not have a permanent dipole, fluctuations of the electron density gives rise to a dipole in a particle
. Bibcode:2010MPLB...24.2679S. doi:10.1142/S0217984910025280.
Media related to Condensed matter physics at Wikimedia Commons
