Mesoscopic variations of local density of states in disordered superconductors

TL;DR

This paper investigates how local density of states correlations in disordered superconductors vary with distance and energy, revealing dependence on symmetry and impurity type, and highlighting similarities to normal metals in specific cases.

Contribution

It provides a detailed analysis of LDoS correlations in different superconductor symmetries and impurity types, emphasizing the role of dimensionality and symmetry in spatial and energy dependence.

Findings

LDoS correlations decay slowly with distance up to phase-breaking length

Long-range behavior depends only on dimensionality, similar to normal metals

Energy dependence of correlations varies with order parameter symmetry and impurity type

Abstract

We explore correlations of inhomogeneous local density of states (LDoS) for impure superconductors with different symmetries of the order parameter (s-wave and d-wave) and different types of scatterers (elastic and magnetic impurities). It turns out that the LDoS correlation function of superconductor always slowly decreases with distance up to the phase-breaking length $l_{\phi}$ and its long-range spatial behavior is determined only by the dimensionality, as in normal metals. On the other hand, the energy dependence of this correlation function is sensitive to symmetry of the order parameter and nature of scatterers. Only in the simplest case of s-wave superconductor with elastic scatterers the inhomogeneous LDoS is directly connected to the corresponding characteristics of normal metal.