The quantum Hall effect in graphene - a theoretical perspective

TL;DR

This paper reviews the theoretical understanding of the quantum Hall effect in graphene, highlighting how its relativistic charge carriers influence the phenomenon compared to traditional two-dimensional electron systems.

Contribution

It provides a comparative theoretical analysis of the quantum Hall effect in graphene versus conventional systems, emphasizing the role of Dirac equation description for graphene's carriers.

Findings

Hall resistance quantization is universal in graphene and conventional systems.

Relativistic and non-relativistic carriers both exhibit quantized Hall resistance.

The effect's universality persists despite fundamental differences in carrier dynamics.

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.