Two-particle spectral function for disordered s-wave superconductors: local maps and collective modes

TL;DR

This paper predicts the local two-particle spectral function in disordered s-wave superconductors, revealing how scanning Josephson spectroscopy maps the order parameter and characterizes collective modes like the Higgs mode under disorder.

Contribution

It provides the first testable predictions linking local spectral functions with disorder effects and distinguishes Higgs and phase modes in disordered superconductors.

Findings

Scanning Josephson spectroscopy maps the local order parameter.

Higgs mode appears as a non-dispersive subgap feature at low momenta.

Amplitude-phase mixing remains small at low momenta despite disorder.

Abstract

We make the first testable predictions for the local two-particle spectral function of a disordered s-wave superconductor, probed by scanning Josephson spectroscopy (sjs), providing complementary information to scanning tunneling spectroscopy (sts). We show that sjs provides a direct map of the local superconducting order parameter that is found to be anticorrelated with the gap map obtained by sts. Furthermore, this anticorrelation increases with disorder. For the momentum resolved spectral function, we find the Higgs mode shows a non-dispersive subgap feature at low momenta, spectrally separated from phase modes, for all disorder strengths. The amplitude-phase mixing remains small at low momenta even when disorder is large. Remarkably, even for large disorder and high momenta, the amplitude-phase mixing oscillates rapidly in frequency and hence do not affect significantly the purity of the Higgs and phase dominated response functions.