Impurity States in D-wave Superconductors

TL;DR

This paper investigates how atomic impurities affect the order parameter and excitation spectrum in d-wave superconductors, revealing bound states, pair-breaking effects, and interference phenomena like Tomasch oscillations.

Contribution

It provides a detailed analysis of impurity-induced bound states and their impact on the spectral properties of d-wave superconductors, highlighting the role of multiple Andreev scattering.

Findings

Impurities create bound quasiparticle states with exponential decay away from the impurity.

Impurities cause local suppression of the superconducting order parameter.

Tomasch oscillations are observed in the continuum spectrum due to quasiparticle interference.

Abstract

The structure of the order parameter and the excitation spectrum are investigated for isolated impurities in d-wave superconductors. Atomic scale impurities, or defects, scatter quasiparticles and lead to local suppression (pair-breaking) near the impurity. The pair-breaking effect arises from the formation of quasiparticle states bound to the impurity. The corresponding reduction in spectral weight in the pair condensate is responsible for pair-breaking. The formation of the bound state is due to multiple Andreev scattering by the combined effects of potential scattering, which leads to changes in momentum of the scattered quasiparticle, and the anisotropy of the d-wave order on the Fermi surface. The spectral weight of the bound state decays exponentially away from the impurity on a length scale $\xi_{*}=\hbar v_f/ \sqrt{|\Delta({\bf p}_f)|^2-\varepsilon_{*}^2}$, where $\varepsilon_{*}$ is the energy of the impurity state. The continuum spectrum exhibits Tomasch oscillations due to the interference between Andreev reflected particle- and hole-like quasiparticles.