Tails of the density of states of two‐dimensional Dirac fermions

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/m2, where gis the strength of disorder and mthe 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.