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We study the two-particle spectral functions and collective modes of weaklydisordered superconductors using a disordered attractive Hubbard model onsquare lattice. We show that the disorder induced scattering between collectivemodes leads to a finite subgap spectral weight in the long wavelength limit. Ingeneral, the spectral weight is distributed between the phase and the Higgschannels, but as we move towards half-filling the Higgs contribution dominates.The inclusion of the density fluctuations lowers the frequency at which thismode occurs, and results in the phase channel gaining a larger contribution tothis subgap mode. Near half-filling, the proximity of the system to the chargedensity wave (CDW) instability leads to strong fluctuations of the effectivedisorder at the commensurate wave-vector ($[\pi,\pi]$). We develop ananalytical mode coupling approach where the pure Goldstone mode in the longwavelength limit couples to the collective mode at $[\pi,\pi]$. This providesinsight into the location and distribution of the two-particle spectral weightsbetween the Higgs and the phase channels.

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