Quasiparticle density of states in dirty high-T_c superconductors

TL;DR

This paper investigates the quasiparticle density of states in dirty high-T_c superconductors, revealing quantum interference effects, localization behavior, and critical singularities near the transition, with implications for experimental observations.

Contribution

It provides a detailed analysis of the density of states in disordered d-wave superconductors, including singular corrections, localization effects, and universal scaling functions, extending understanding beyond conventional Anderson localization.

Findings

Density of states vanishes in localized phase as |E| or E^2 depending on symmetry.

Exact universal scaling function for crossover from ballistic to localized regimes in 1D.

Critical singularities in the density of states near the localization transition in higher dimensions.

Abstract

We study the density of quasiparticle states of dirty d-wave superconductors. We show the existence of singular corrections to the density of states due to quantum interference effects. We then argue that the density of states actually vanishes in the localized phase as $|E|$ or $E^2$ depending on whether time reversal is a good symmetry or not. We verify this result for systems without time reversal symmetry in one dimension using supersymmetry techniques. This simple, instructive calculation also provides the exact universal scaling function for the density of states for the crossover from ballistic to localized behaviour in one dimension. Above two dimensions, we argue that in contrast to the conventional Anderson localization transition, the density of states has critical singularities which we calculate in a $2+\epsilon$ expansion. We discuss consequences of our results for various experiments on dirty high-$T_c$ materials.