PERTURBATIVE EVIDENCE OF NON-UNIVERSALITY IN THE QUANTIZED HALL CONDUCTIVITY OF A DISORDERED RELATIVISTIC 2D ELECTRON GAS

Abstract

We study a relativistic two-dimensional electron gas in the presence of a uniform external magnetic field and a random static scalar potential. We compute, in first order perturbation theory, the averages of the charge density and of the transverse conductivity for a white-noise potential, and show that, within this treatment, their quantized values are modified by the disorder. One of the most puzzling features of the quantum Hall effect (QHE) 1 is the apparent insensitivity of the quantization of the Hall conductivity σH (in units of e 2 /h) with respect to type of host material, sample geometry, presence of impurities or defects, etc. Being such a high precision phenomenon, it is important to investigate possible deviations from the quantized values of σH. So far, theoretical investigations have been concerned mostly with the effects of disorder, 2 and they all seem to agree that the QHE is robust with respect to it. Another possible correction to the QHE is of relativistic origin: if most of the current is carried by few electrons because of localization, or if it is carried mainly by electrons in edg

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