2010/04/30 by M. O. Goerbig · 975 citations
Materials Science · Physics and Astronomy · #Composite fermion #Condensed matter physics #Dirac fermion #Electron #Fermi gas #Fermion #Fractional quantum Hall effect #Graphene #Graphene research and applications #Landau quantization #Magnetic field #Physics #Quantization (signal processing) #Quantum Hall effect #Quantum and electron transport phenomena #Quantum electrodynamics #Quantum mechanics #Quantum oscillations #Quantum spin Hall effect #Topological Materials and Phenomena #cond-mat.mes-hall #cond-mat.str-el
paper · pdf · doi:10.1103/revmodphys.83.1193
published in Reviews of Modern Physics 83(4), 1193-1243 (American Physical Society) · 56 pages, 27 figures; published version with minor corrections and updated references
openalex publication_date 2011/11/03 · arxiv created 2011/11/22 · arxiv updated 2011/11/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 weak-coupling 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 electron-phonon 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.