Gap fluctuations in inhomogeneous superconductors

Spatial fluctuations of the effective pairing interaction between electrons in a superconductor induce variations of the order parameter that in turn lead to significant changes in the density of states. In addition to an overall reduction of the quasiparticle energy gap, theory suggests that mesoscopic fluctuations of the impurity potential induce localized tail states below the mean-field gap edge. Using a field theoretic approach, we elucidate the nature of the states in the "subgap" region. Specifically, we show that these states are associated with replica-nontrivial instanton solutions of the mean-field equations.