Density of States below the Thouless Gap in a Mesoscopic SNS Junction

Quasiclassical theory predicts an existence of a sharp energy gap E_g \sim D/L^2 in the excitation spectrum of a long diffusive superconductor--normal metal--superconductor (SNS) junction. We show that mesoscopic fluctuations remove the sharp edge of the spectrum, leading to a nonzero DoS for all energies. Physically, this effect originates from the quasi-localized states in the normal metal. Technically, we use an extension of Efetov's supermatrix sigma-model for mixed NS systems. We demonstrate the equivalence of the supersymmetric saddle-point solution to the standard quasiclassical Usadel solution, and show that the instanton solution with broken supersymmetry provides a non-zero DoS at energies E < E_g.