Disorder Effects in Two-Dimensional d-wave Superconductors

TL;DR

This paper investigates how weak nonmagnetic impurities affect the density of states in two-dimensional d-wave superconductors, revealing a nontrivial power-law behavior near the Fermi energy and linking symmetry properties to the density of states at zero energy.

Contribution

It introduces a nonperturbative approach using replica trick and bosonization to analyze disorder effects, showing the density of states follows a power-law near the Fermi energy in d-wave superconductors.

Findings

Density of states follows a power-law near the Fermi energy: $ ho() o ||^{}$.

The zero-energy density of states $ ho(0)$ is zero due to continuous symmetry.

Disorder can induce a finite $ ho(0)$ in models with discrete symmetry, like orbital antiferromagnets.

Abstract

Influence of weak nonmagnetic impurities on the single-particle density of states $\rho(\omega)$ of two-dimensional electron systems with a conical spectrum is studied. We use a nonperturbative approach, based on replica trick with subsequent mapping of the effective action onto a one-dimensional model of interacting fermions, the latter being treated by Abelian and non-Abelian bosonization methods. It is shown that, in a d-wave superconductor, the density of states, averaged over randomness, follows a nontrivial power-law behavior near the Fermi energy: $\rho(\omega) \sim |\omega|^{\alpha}$. The exponent $\alpha>0$ is calculated for several types of disorder. We demonstrate that the property $\rho(0) = 0$ is a direct consequence of a {\it continuous} symmetry of the effective fermionic model, whose breakdown is forbidden in two dimensions. As a counter example, we consider another model with a conical spectrum - a two-dimensional orbital antiferromagnet, where static disorder leads to a finite $\rho(0)$ due to breakdown of a {\it discrete} (particle-hole) symmetry.