Theory of Interaction Effects in N-S Junctions out of Equilibrium

TL;DR

This paper develops a theoretical framework for understanding how non-equilibrium electron fluctuations in N-S junctions alter the superconductor's density of states, explaining experimental observations of spectral broadening.

Contribution

It introduces a novel theory linking non-equilibrium fluctuations to phase fluctuations in N-S junctions, explaining the broadening of the density of states.

Findings

Non-equilibrium fluctuations cause phase fluctuations in the superconductor.

Density of states in the superconductor deviates from BCS form under non-equilibrium.

Proposes an experiment to test the theoretical explanation.

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 non-equilibrium 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 non-equilibrium, and can be described in terms of a low energy collective mode of the junction, which couples normal currents in N-layer and supercurrents. This mode is analogous to the Schmid-Sch\"{o}n mode. To interpret their measurements of the tunneling current, Pothier {\em et. al} [Phys. Rev. Lett. {\bf 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 manifest itself similarly to the broadening of the distribution function. Mechanism suggested here can be a possible explanation of this experimental puzzle. We also propose an independent experiment to test our explanation.