On the theory of Josephson effect in a diffusive tunnel junction

TL;DR

This paper theoretically analyzes the equilibrium Josephson current in diffusive superconductors, revealing localized excitation states near the barrier and providing a detailed perturbation theory expansion for the current.

Contribution

It introduces a new understanding of localized states and the perturbation expansion parameter in diffusive Josephson junctions, differing from ballistic cases.

Findings

Localized states form near the tunnel barrier in diffusive junctions.

The Josephson current involves a broad spectral region near the energy gap.

The perturbation expansion parameter is larger than the tunneling probability, W.

Abstract

Specific features of the equilibrium current-carrying state of a Josephson tunnel junction between diffusive superconductors are studied theoretically in the 1D geometry. It is found that the Josephson current induces localized states of electron excitations in the vicinity of the tunnel barrier, which are a continuous analog of Andreev levels in a ballistic junction. The depth of the corresponding ``potential well'' is much greater than the separation between an Andreev level and the continuous energy spectrum boundary for the same transmissivity of the barrier. In contrast to a ballistic junction in which the Josephson current is transported completely by localized excitations, the contribution to current in a diffusive junction comes from whole spectral region near the energy gap boundary, where the density of states differs considerably from its unperturbed value. The correction to the Josephson current in the second order of the barrier transmissivity, which contains the second harmonic of the phase jump, is calculated and it is found that the true expansion parameter of the perturbation theory for a diffusive junction is not the tunneling probability $\Gamma$ itself, but a much larger parameter $W = (3\xi_0/4l)\Gamma$.