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Abstract: We review the basic aspects of electrons in graphene two-dimensionalgraphite exposed to a strong perpendicular magnetic field. One of its mostsalient features is the relativistic quantum Hall effect the observation ofwhich has been the experimental breakthrough in identifying pseudo-relativisticmassless charge carriers as the low-energy excitations in graphene. The effectmay be understood in terms of Landau quantization for massless Dirac fermions,which is also the theoretical basis for the understanding of more involvedphenomena due to electronic interactions. We present the role ofelectron-electron interactions both in the weak-coupling limit, where theelectron-hole excitations are determined by collective modes, and in thestrong-coupling regime of partially filled relativistic Landau levels. In thelatter limit, exotic ferromagnetic phases and incompressible quantum liquidsare expected to be at the origin of recently observed fractional quantum Hallstates. Furthermore, we discuss briefly the electron-phonon coupling in astrong magnetic field. Although the present review has a dominating theoreticalcharacter, a close connection with available experimental observation isintended.



Author: M. O. Goerbig

Source: https://arxiv.org/







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