The quantum Hall effect in graphene - a theoretical perspective

Abstract

This short theoretical review deals with some essential ingredients for the understanding of the quantum Hall effect in graphene in comparison with the effect in conventional two-dimensional electron systems with a parabolic band dispersion. The main difference between the two systems stems from the "ultra-relativistic" character of the low-energy carriers in graphene, which are described in terms of a Dirac equation, as compared to the non-relativistic Schrödinger equation used for electrons with a parabolic band dispersion. In spite of this fundamental difference, the Hall resistance quantisation is universal in the sense that it is given in terms of the universal constant h/e^2 and an integer number, regardless of whether the charge carriers are characterised by Galilean or Lorentz invariance, for non-relativistic or relativistic carriers, respectively.

9 pages, 4 figures; brief review article for Comptes Rendus de l'Academie des Sciences; references added with respect to previous version

References in corpus (14)

• The structure of suspended graphene sheets
• Chiral tunneling and the Klein paradox in graphene
• Landau Level Splitting in Graphene in High Magnetic Fields
• Multicomponent fractional quantum Hall effect in graphene
• Edge States and the Quantized Hall Effect in Graphene
• Dissipative Quantum Hall Effect in Graphene near the Dirac Point
• Epitaxial Graphene Electronic Structure And Transport
• Measurement of the ν= 1/3 fractional quantum Hall energy gap in suspended graphene
• Analysis of a SU(4) generalization of Halperin's wave function as an approach towards a SU(4) fractional quantum Hall effect in graphene sheets
• WKB analysis of edge states in graphene in a strong magnetic field
• The plasma picture of the fractional quantum Hall effect with internal SU(K) symmetries
• Unveiling quantum Hall transport by Efros-Shklovskii to Mott variable range hopping transition with Graphene
• High magnetic field theory for the local density of states in graphene with smooth arbitrary potential landscapes
• Measurement of beauty production in DIS and F_2^bbbar extraction at ZEUS

Cited by in corpus (13)

• CODATA Recommended Values of the Fundamental Physical Constants: 2010
• Single-electron current sources: towards a refined definition of ampere
• Phase diagram for the $\nu =0$ quantum Hall state in monolayer graphene
• Generalized effective hamiltonian for graphene under non-uniform strain
• Direct observation of photonic Landau levels and helical edge states in strained honeycomb lattices
• Edge excitations of the canted antiferromagnetic phase of the $\nu =0$ quantum Hall state in graphene: a simplified analysis
• Effective model for Majorana modes in graphene
• Effect of electronic band dispersion curvature on de Haas-van Alphen oscillations
• Integer Quantum Hall Effect in Graphene Channel with p-n Junction at Domain Wall in Ferroelectric Substrate
• Spectrum of edge states in the $\nu =0$ quantum Hall phases in graphene
• Strain engineering of ferromagnetic-graphene-ferroelectric nanostructures
• Klein tunneling degradation and enhanced Fabry-Pérot interference in graphene/h-BN moiré-superlattice devices
• Nontrivial magnetic field related phenomena in the single-layer graphene on ferroelectric substrate