On the theory of Josephson effect in a diffusive tunnel junction

Specific features of the equilibrium current-carrying state of a Josephsontunnel junction between diffusive superconductors are studied theoretically inthe 1D geometry. It is found that the Josephson current induces localizedstates of electron excitations in the vicinity of the tunnel barrier, which area continuous analog of Andreev levels in a ballistic junction. The depth of thecorresponding ``potential well'' is much greater than the separation between anAndreev level and the continuous energy spectrum boundary for the sametransmissivity of the barrier. In contrast to a ballistic junction in which theJosephson current is transported completely by localized excitations, thecontribution to current in a diffusive junction comes from whole spectralregion near the energy gap boundary, where the density of states differsconsiderably from its unperturbed value. The correction to the Josephsoncurrent in the second order of the barrier transmissivity, which contains thesecond harmonic of the phase jump, is calculated and it is found that the trueexpansion parameter of the perturbation theory for a diffusive junction is notthe tunneling probability $\Gamma$ itself, but a much larger parameter $W =(3\xi_0/4l)\Gamma$.Comment: 8 pages, 5 Postscript figures, submitted to Low Temp. Phy