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 Schr\"odinger 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.