Electron states in a magnetic field
Cambridge : Cambridge University Press
InKatsnelson, M.I. (ed.), The Physics of Graphene ((Second Edition), pp. 24-62
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Theory of Condensed Matter
Katsnelson, M.I. (ed.), The Physics of Graphene ((Second Edition)
SubjectTheory of Condensed Matter
The chapter starts with the derivation of effective Hamiltonian for band electrons in magnetic field and continues with discussion of energy levels in magnetic field for massless Dirac fermions. The case of bilayer graphene is also considered. Special attention is paid to a formation of topologically protected zero-energy modes. Using band electrons in magnetic field as an example, a general concept of Berry phase is introduced. Magneto-oscillation effects for two-dimensional Dirac fermions are considered. Quantum Hall effect is discussed, via topological approach by Thouless and coworkers. At the end, we discuss electronic structure in the presence of crossed electric and magnetic fields and the effects of a smooth disorder on Landau levels for massless Dirac electrons.
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