Inhomogeneity correlations in dirty superconductors, I

Abstract

It is shown that fluctuations δ‡ around the impurity averaged superconducting order parameter 〈Δ〉 can be large due to interplay of disorder and (decoupled) interaction. Correlations 〈(δΔ)2〉 exceeding a critical value render superconductors with nonmagnetic impurities gapless. In addition to a mixed phase, 〈Δ〉≠0 andMΔ≠0, a superconducting glass phase with 〈Δ〉=0 andMΔ≠0 is derived. In general, correlations 〈(δΔ)2〉 emerge from nonperturbative, saddle point solutions of a replicated matrix field theory. Replica symmetry, soft modes, and other order parameters are discussed.