Theory of interaction effects in normal-metal–superconductor junctions out of equilibrium

Abstract

We consider a normal-metal–superconductor (N-S) junction in the regime when electrons in the normal metal are driven out of equilibrium. We show that the nonequilibrium fluctuations of the electron density in the N layer cause the fluctuations of the phase of the order parameter in the S layer. As a result, the density of states in the superconductor deviates from the BCS form; most notably the density of states in the gap becomes finite. This effect can be viewed as a result of the time-reversal symmetry breaking due to the nonequilibrium, and can be described in terms of a low-energy collective mode of the junction, which couples normal currents in N-layer current and supercurrent. This mode is analogous to the Schmid-Schön mode. To interpret their measurements of the tunneling current, Pothier et al. [Phys. Rev. Lett. 79, 3490 (1997)] had to assume that the energy relaxation rate in the normal metal is surprisingly high. The broadening of the BCS singularity of the density of states in the S layer manifests itself similarly to the broadening of the distribution function. The mechanism suggested here can be a possible explanation of this experimental puzzle. We also propose an independent experiment to test our explanation.

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