Quantum Hall plateau transition in the lowest Landau level of disordered graphene

TL;DR

This paper analyzes how disorder affects the density of states and localization properties in the lowest Landau level of graphene, revealing unique universality classes for the quantum Hall plateau transition.

Contribution

It provides an exact analytical calculation of the density of states and identifies the localization-delocalization transition in disordered relativistic fermions in graphene.

Findings

Exact density of states for Lorentzian disorder distribution

Identification of a distinct universality class for the LD transition

Relevance to integer quantum Hall plateau transitions in graphene

Abstract

We investigate, analytically and numerically, the effects of disorder on the density of states and on the localization properties of the relativistic two dimensional fermions in the lowest Landau level. Employing a supersymmetric technique, we calculate the exact density of states for the Cauchy (Lorentzian) distribution for various types of disorders. We use a numerical technique to establish the localization-delocalization (LD) transition in the lowest Landau level. For some types of disorder the LD transition is shown to belong to a different universality class, as compared to the corresponding nonrelativistic problem. The results are relevant to the integer quantum Hall plateau transitions observed in graphene.