Landau levels
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In quantum mechanics, the energies of cyclotron orbits of charged particles in a uniform magnetic field are quantized to discrete values, thus known as Landau levels. These levels are degenerate, with
Diagram of a cyclotron orbit of a particle with speed v, which is the classical trajectory of a charged particle (here positive charge) under a uniform magnetic field B. The Landau quantization refers to a quantum charged particle under a uniform magnetic field.
Graphene
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Graphene is a variety of the element carbon which occurs naturally in small amounts. In graphene, the carbon forms a sheet of interlocked atoms as hexagons one carbon atom thick. The result resembles
Graphene is an atomic-scale honeycomb structure made of carbon atoms
Andre Geim and Konstantin Novoselov at the Nobel Laureate press conference, Royal Swedish Academy of Sciences, 2010.
Scanning probe microscopy image of graphene
Photograph of single-layer graphene oxide undergoing high temperature chemical treatment, resulting in sheet folding and loss of carboxylic functionality, or through room temperature carbodiimide treatment, collapsing into star-like clusters.