DISORDER EFFECTS IN 2-DIMENSIONAL FERMI SYSTEMS WITH CONICAL SPECTRUM- EXACT RESULTS FOR THE DENSITY-OF-STATES

The influence of weak non-magnetic disorder on the single-particle den sity of states rho(omega) of two-dimensional electron systems with a c onical spectrum is studied. We use a non-perturbative approach, based on the replica trick with subsequent mapping of the effective action o nto a one-dimensional model of interacting fermions, the latter being treated by abelian and non-abelian bosonization methods. Specifically, we consider a weakly disordered p- or d-wave superconductor, in which case the problem reduces to a model of (2+1)-dimensional massless Dir ac fermions coupled to random, static, generally non-abelian gauge fie lds. It is shown that the density of states of a two-dimensional p- or d-wave superconductor, averaged over randomness, follows a non-trivia l power-law behavior near the Fermi energy: rho(omega) similar to \w\( alpha). The exponent alpha > 0 is exactly calculated for several types of disorder, We demonstrate that the property rho(0) = 0 is a direct consequence of a continuous symmetry of the effective fermionic model, whose breakdown is forbidden in two dimensions. As a counter example, we also discuss another model with a conical spectrum - a two-dimensi onal orbital antiferromagnet where static disorder leads to a finite r ho(0) due to the breakdown of a discrete (particle-hole) symmetry.