Universality, exponents and anomaly cancellation in disordered Dirac fermions

TL;DR

This paper investigates how short-range correlated disorder and momentum cut-offs affect disordered 2D Dirac fermions, revealing that universality in conductivity depends on removing ultraviolet cut-offs due to anomaly cancellations.

Contribution

It introduces a more realistic model of disordered Dirac fermions by including short-range correlations and momentum cut-offs, analyzing their impact on physical properties.

Findings

Density of states exhibits anomalous critical behavior dependent on disorder.

Conductivity is universal only when ultraviolet cut-offs are removed.

Supersymmetric anomaly cancellation explains the universality conditions.

Abstract

Disordered 2D chiral fermions provide an effective description of several materials including graphene and topological insulators. While previous analysis considered delta correlated disorder and no ultraviolet cut-offs, we consider here the effect of short range correlated disorder and the presence of a momentum cut-off, providing a more realistic description of condensed matter models. We show that the density of states is anomalous with a critical exponent function of the disorder and that conductivity is universal only when the ultraviolet cut-off is removed, as consequence of the supersymmetric cancellation of the anomalies.