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-dimensi onal lattice is considered. We give the explicit asymptotic form of the sin gle-electron density of states as a function of both energy and (average) D irac mass, in the regime where all states are localized. We make use of a w eak-disorder expansion in the parameter g/m(2), where g is the strength of disorder and m the avt rag Dirac mass for the case in which the evaluation of the (supersymmetric) integrals corresponds to non-uniform solutions of t he saddle point equation. The resulting density of states has tails which d eviate from the typical pure Gaussian form by an analytic prefactor.