Impurity States and the Absence of Quasiparticle Localization in Disordered D-Wave Superconductors

TL;DR

This paper demonstrates that in disordered d-wave superconductors, impurity states remain extended due to power-law decay, preventing quasiparticle localization regardless of impurity concentration.

Contribution

It reveals that unitary impurities create zero-energy states with power-law decay, leading to extended quasiparticle states and preventing localization in disordered d-wave superconductors.

Findings

Impurity states decay as a power-law along d-wave nodes.

Extended quasiparticle states exist below a certain energy scale.

The characteristic energy scale decreases exponentially with impurity density.

Abstract

The absence of localization of impurity-induced low-energy quasiparticle states in a two-dimensional $d$-wave superconductor is argued for any amount of disorder in the limit of unitary scatterers. This surprising result follows from the fact that a unitary impurity produces a marginally-bound state at zero energy which decays as a power-law along the nodes of the $d$-wave energy gap. Consequently, for finite density of impurities, the impurity-induced states are coupled by long-range overlaps yielding extended quasiparticle states below a characteristic energy scale $\omega_c$. Simple scaling arguments suggest that $\omega_c \propto e^{-c/n_{\rm imp}}$, where $n_{\rm imp}$ is the impurity density and $c$ is a positive constant.