Quantized Hall conductance in a relativistic two-dimensional electron gas

Abstract

The formula for the quantized Hall conductance in a two-dimensional electron gas is often derived by solving the Schrödinger equation for an electron in crossed electric and magnetic fields, and taking the expectation value of the current operator in its eigenstates. In this report we demonstrate explicitly, by using the Dirac equation, that there are no relativistic corrections to this expression, at least in the ideal case. This is true even if the drift velocity of the electrons approaches the speed of light or the Landau level splitting approaches the electron rest-mass energy and holds despite the appearance of a classical correction to the cyclotron frequency.