The basic aspects of electrons in graphene (two-dimensional graphite) exposed to a strong perpendicular magnetic field are reviewed. One of its most salient features is the relativistic quantum Hall effect, the observation of which has been the experimental breakthrough in identifying pseudorelativistic massless charge carriers as the low-energy excitations in graphene. The effect may be understood in terms of Landau quantization for massless Dirac fermions, which is also the theoretical basis for the understanding of more involved phenomena due to electronic interactions. The role of electron-electron interactions both in the weakcoupling limit, where the electron-hole excitations are determined by collective modes, and in the strong-coupling regime of partially filled relativistic Landau levels are presented. In the latter limit, exotic ferromagnetic phases and incompressible quantum liquids are expected to be at the origin of recently observed (fractional) quantum Hall states. Furthermore, the electronphonon coupling in a strong magnetic field is discussed. Although the present review has a dominant theoretical character, a close connection with available experimental observation is intended.
We study under which general conditions a pair of Dirac points in the
electronic spectrum of a two-dimensional crystal may merge into a single one.
The merging signals a topological transition between a semi-metallic phase and
a band insulator. We derive a universal Hamiltonian that describes the physical
properties of the transition, which is controlled by a single parameter, and
analyze the Landau-level spectrum in its vicinity. This merging may be observed
in the organic salt alpha-(BEDT-TTF)_2 I_3 or in an optical lattice of cold
atoms simulating deformed graphene.Comment: 4 pages, 5 figures
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