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

TL;DR

This paper investigates the phase diagram of disordered 2D Majorana quasiparticles in class D, revealing a metallic phase emerging from free Majorana fermions and analyzing the effects of vortex disorder on the density of states.

Contribution

It develops a supersymmetric nonabelian bosonization approach to study 2D disordered Majorana fermions and maps the problem onto a nonlinear sigma model including a Z_2 degree of freedom.

Findings

Identification of a 2D metallic phase originating from free Majorana fermions.

Agreement of density of states with random-matrix predictions in the ergodic limit.

Vortex disorder alters low-energy density of states and shifts the symmetry class to BD.

Abstract

Disordered noninteracting quasiparticles that are governed by a Majorana-type Hamiltonian -- prominent examples are dirty superconductors with broken time-reversal and spin-rotation symmetry, or the fermionic representation of the 2d Ising model with fluctuating bond strengths -- are called class D. In two dimensions, weakly disordered systems of this kind may possess a metallic 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 this result, we develop a supersymmetric extension of the method of nonabelian bosonization. On the metallic side of the metal-insulator transition, the density of states becomes nonvanishing at zero energy, by a mechanism akin to dynamical mass generation. This feature is explored in a model of N species of disordered Dirac fermions, via the mapping on a nonlinear sigma model, which encapsulates a Z_2 spin degree of freedom. We compute the density of states in a finite system, and obtain agreement with the random-matrix prediction for class D, in the ergodic limit. Vortex disorder, which is a relevant perturbation at the free-fermion point, changes the density of states at low energy and suppresses the local Z_2 degree of freedom, thereby leading to a different symmetry class, BD.