Tails of Localized Density of States of Two-dimensional Dirac Fermions

TL;DR

This paper derives the asymptotic form of the density of states for two-dimensional Dirac fermions with random mass, revealing localized states and non-Gaussian tail behavior in the density of states.

Contribution

It provides an explicit asymptotic expression for the density of states considering disorder effects in 2D Dirac fermions, using a weak-disorder expansion and supersymmetric integrals.

Findings

Density of states exhibits localized state tails.

Tails deviate from Gaussian form with an analytic prefactor.

Results applicable in regimes of weak disorder and localized states.

Abstract

The density of states of Dirac fermions with a random mass on a two-dimensional lattice is considered. We give the explicit asymptotic form of the single-electron density of states as a function of both energy and (average) Dirac mass, in the regime where all states are localized. We make use of a weak-disorder expansion in the parameter g/m^2, where g is the strength of disorder and m the average Dirac mass for the case in which the evaluation of the (supersymmetric) integrals corresponds to non-uniform solutions of the saddle point equation. The resulting density of states has tails which deviate from the typical pure Gaussian form by an analytic prefactor.