Disordered 2d quasiparticles in class D: Dirac fermions with random mass, and dirty superconductors

Disordered noninteracting quasiparticles that are governed by a Majorana-ty pe Hamiltonian prominent examples are dirty superconductors with broken tim e-reversal and spin-rotation symmetry, or the fermionic representation of t he 2d Ising model with fluctuating bond strengths - are called class D. In two dimensions, weakly disordered systems of this kind may possess a metall ic phase beyond the insulating phases expected for strong disorder. We show that the 2d metal phase emanates from the free Majorana fermion point, in the direction of the RG trajectory of a perturbed WZW model. To establish t his result, we develop a supersymmetric extension of the method of nonabeli an bosonization. On the metallic side of the metal-insulator transition, th e density of states becomes nonvanishing at zero energy, by a mechanism aki n to dynamical mass generation. This feature is explored in a model of N sp ecies of disordered Dirac fermions, via the mapping on a nonlinear sigma mo del, which encapsulates a Z(2) spin degree of freedom. We compute the densi ty of states in a finite system, and obtain agreement with the random-matri x prediction for class D, in the ergodic limit. Vortex disorder, which is a relevant perturbation at the free-fermion point, changes the density of st ates at low energy and suppresses the local Z2 degree of freedom, thereby l eading to a different symmetry class, BD. (C) 2000 Elsevier Science B.V. Al l rights reserved.