Role of the impurity-potential range in disordered d-wave superconductors

TL;DR

This paper investigates how the range of disorder influences quasiparticle localization in disordered d-wave superconductors, revealing that long-range disorder leads to unique topological effects and a crossover to different behaviors with short-range components.

Contribution

It provides a unified non-linear sigma-model framework that accounts for the effects of disorder range on quasiparticle properties in d-wave superconductors.

Findings

Long-range disorder induces intra-node scattering and topological effects.

Purely long-range disorder results in vanishing density of states.

Short-range disorder introduces internode scattering, altering localization properties.

Abstract

We analyze how the range of disorder affects the localization properties of quasiparticles in a two-dimensional d-wave superconductor within the standard non-linear sigma-model approach to disordered systems. We show that for purely long-range disorder, which only induces intra-node scattering processes, the approach is free from the ambiguities which often beset the disordered Dirac-fermion theories, and gives rise to a Wess-Zumino-Novikov-Witten action leading to vanishing density of states and finite conductivities. We also study the crossover induced by internode scattering due to a short range component of the disorder, thus providing a coherent non-linear sigma-model description in agreement with all the various findings of different approaches.