Quantum interference in nested d-wave superconductors: a real-space perspective

TL;DR

This paper investigates quantum interference effects in d-wave superconductors with impurities, revealing zero-energy states and their implications for cuprate models through analytical and numerical methods.

Contribution

It provides a detailed analysis of impurity-induced quantum interference and zero-energy states in d-wave superconductors, clarifying controversial aspects of the particle-hole symmetric model.

Findings

Existence of a zero-energy delta function in the density of states.

Resonant impurity states are sublattice-specific.

Quantum interference significantly affects local density of states.

Abstract

We study the local density of states around potential scatterers in d-wave superconductors, and show that quantum interference between impurity states is not negligible for experimentally relevant impurity concentrations. The two impurity model is used as a paradigm to understand these effects analytically and in interpreting numerical solutions of the Bogoliubov-de Gennes equations on fully disordered systems. We focus primarily on the globally particle-hole symmetric model which has been the subject of considerable controversy, and give evidence that a zero-energy delta function exists in the DOS. The anomalous spectral weight at zero energy is seen to arise from resonant impurity states belonging to a particular sublattice, exactly as in the 2-impurity version of this model. We discuss the implications of these findings for realistic models of the cuprates.