Correlated pair-amplitude fluctuations in disordered BCS superconductors

More than fifty years old "Anderson's theorem" suggests disorder-independent pair-amplitude and critical temperature at low to moderate strength of disorders. In spite of the extension of this paradigm and several subsequent theoretical proposals, mechanism for the superconductor-insulator transition (SIT) at large disorder is still an open problem. The understanding of experimental data at intermediate disorder is also lacking. Here, we proceed beyond "Anderson's theorem" by calculating disorder-averaged two-point pair-amplitude fluctuations. We find this correlation to be finite and long-ranged, activating scattering of quasiparticles in the novel "Cooper" channel. Without invoking any further parameter, this mechanism quantitatively predicts several testable properties: reduction of pair-amplitude at zero temperature; reduction of temperature, T_\Delta, at which pair-amplitude vanishes; suppression and broadening of coherence peak; and decrease of hard-gap in quasiparticle density of states, with the increase of disorder. We interpret old and new data at intermediate disorder in light of our predictions. The robustness of this theory will hopefully provide insight to unravel the true mechanism for SIT.