Exact Density of States in a System of Disordered Two Dimensional Dirac Fermions in the Unitarity Limit: The d-wave Superconductor

TL;DR

This paper introduces a method to compute the exact density of states in disordered 2D Dirac fermion systems, specifically applied to the unitarity limit of d-wave superconductors, revealing additional in-gap states due to impurities.

Contribution

It provides an exact calculation technique for the density of states in disordered 2D Dirac systems, including d-wave superconductors, in the unitarity limit, extending previous approximate methods.

Findings

Additional in-gap states induced by impurities

Density of states characterized by a specific logarithmic divergence

Method applicable to disordered Dirac fermion systems

Abstract

In this paper we present a method to compute the exact density of states induced by $N$ non magnetic impurities in a system of two dimensional Dirac fermions in the unitarity limit. We review the case of the $\pi$-flux phase of the Heisenberg model and also treat the disordered d-wave superconductor. In both case we find additional states in the gap with $\delta \rho (\omega) \simeq n_i/ |\omega(\ln^2 |\omega/\Delta_0| + (\pi/2)^2)|$.