Subgap two-particle spectral weight in disordered $s$-wave superconductors: Insights from mode coupling approach

TL;DR

This paper investigates how disorder affects two-particle spectral functions in s-wave superconductors, revealing subgap spectral weight distribution and mode coupling effects near half-filling through an analytical approach.

Contribution

It introduces a mode coupling approach to analyze the distribution of spectral weight between phase and Higgs modes in disordered superconductors, especially near charge density wave instability.

Findings

Disorder induces finite subgap spectral weight at long wavelengths.

Spectral weight shifts towards the Higgs channel near half-filling.

Mode coupling explains the spectral weight distribution and mode frequencies.

Abstract

We study the two-particle spectral functions and collective modes of weakly disordered superconductors using a disordered attractive Hubbard model on square lattice. We show that the disorder induced scattering between collective modes leads to a finite subgap spectral weight in the long wavelength limit. In general, the spectral weight is distributed between the phase and the Higgs channels, but as we move towards half-filling the Higgs contribution dominates. The inclusion of the density fluctuations lowers the frequency at which this mode occurs, and results in the phase channel gaining a larger contribution to this subgap mode. Near half-filling, the proximity of the system to the charge density wave (CDW) instability leads to strong fluctuations of the effective disorder at the commensurate wave-vector ($[\pi,\pi]$). We develop an analytical mode coupling approach where the pure Goldstone mode in the long wavelength limit couples to the collective mode at $[\pi,\pi]$. This provides insight into the location and distribution of the two-particle spectral weights between the Higgs and the phase channels.