We study the two-particle spectral functions and collective modes of weakly disordered superconductors using a disordered attractive Hubbard model on a 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 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.

• Received 3 June 2022
• Revised 17 August 2022
• Accepted 18 August 2022

DOI:https://doi.org/10.1103/PhysRevB.106.064512