On the theory of Josephson effect in a diffusive tunnel junction

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 $W = (3\xi_0/4l)\Gamma$.Comment: 8 pages, 5 Postscript figures, submitted to Low Temp. Phy

Giant Josephson current through a single bound state in a superconducting tunnel junction

We study the microscopic structure of the Josephson current in a single-mode tunnel junction with a wide quasiclassical tunnel barrier. In such a junction each Andreev bound state carries a current of magnitude proportional to the {\em amplitude} of the normal electron transmission through the junction. Tremendous enhancement of the bound state current is caused by the resonance coupling of superconducting bound states at both superconductor-insulator interfaces of the junction. The possibility of experimental observation of the single bound state current is discussed.Comment: 11 pages, [aps,preprint]{revtex

Topological properties of superconducting junctions

Motivated by recent developments in the field of one-dimensional topological superconductors, we investigate the topological properties of s-matrix of generic superconducting junctions where dimension should not play any role. We argue that for a finite junction the s-matrix is always topologically trivial. We resolve an apparent contradiction with the previous results by taking into account the low-energy resonant poles of s-matrix. Thus no common topological transition occur in a finite junction. We reveal a transition of a different kind that concerns the configuration of the resonant poles

Resonant transmission of normal electrons through Andreev states in ferromagnets

Giant oscillations of the conductance of a superconductor - ferromagnet - superconductor Andreev interferometer are predicted. The effect is due to the resonant transmission of normal electrons through Andreev levels when the voltage $V$ applied to the ferromagnet is close to $2h_0/e$ ($h_0$ is the spin-dependant part of the electron energy). The effect of bias voltage and phase difference between the superconductors on the current and the differential conductance is presented. These efects allow a direct spectroscopy of Andreev levels in the ferromagnet.Comment: 4 pages, 4 figure

Local Electronic Structure of Defects in Superconductors

The electronic structure near defects (such as impurities) in superconductors is explored using a new, fully self-consistent technique. This technique exploits the short-range nature of the impurity potential and the induced change in the superconducting order parameter to calculate features in the electronic structure down to the atomic scale with unprecedented spectral resolution. Magnetic and non-magnetic static impurity potentials are considered, as well as local alterations in the pairing interaction. Extensions to strong-coupling superconductors and superconductors with anisotropic order parameters are formulated.Comment: RevTex source, 20 pages including 22 figures in text with eps

Incomplete Andreev reflection in a clean Superconductor/Ferromagnet/Superconductor junction

We study the Josephson effect in a clean Superconductor-Ferromagnet-Superconductor junction for arbitrarily large spin polarizations. The Andreev reflection at a clean Ferromagnet-Superconductor interface is incomplete, and Andreev channels with a large incidence angle are progressively suppressed with increasing exchange energy. As a result, the critical current exhibits oscillations as a function of the exchange energy and of the length of the ferromagnet and has a temperature dependence which deviates from the one predicted by the quasiclassical theory