On the theory of Josephson effect in a diffusive tunnel junction

Abstract

Specific features of the equilibrium current-carrying state of a Josephson tunnel junction between diffusive superconductors (with the electron mean free path l smaller than the coherence length ξ0) are studied theoretically in the 1D geometry when the current does not spread in the junction banks. It is shown that the concept of “weak link” with the phase jump Φ∼1 of the order parameter exists only for a low transmissivity of the barrier Γ≪l/ξ0≪1. Otherwise, the presence of the tunnel junction virtually does not affect the distributions of the order parameter modulus and phase. It is found that the Josephson current flowing in the vicinity of the tunnel barrier induces localized states of electron excitations, which are a continuous analog of Andreev’s levels in a ballistic junction. The depth of the corresponding “potential well” is much larger than the separation between an Andreev’s 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 the entire spectral region near the energy gap boundary, where the density of states differs considerably from its unperturbed value. The correction to the Josephson j(Φ) in the second order of the barrier transmissivity, which contains the second harmonic of the phase jump Φ, is calculated and it is found that the true expansion parameter j(Φ) of the perturbation theory for a diffusive junction is not the tunneling probability Γ, but a much larger parameter W=(3ξ0/4l)Γ. This simplifies the conditions for the experimental observation of higher harmonics of j(Φ) in junctions with controllable transmissivity of the barrier.