A Diagrammatic Theory of Random Scattering Matrices for Normal-Superconducting Mesoscopic Junctions

The planar-diagrammatic technique of large-$N$ random matrices is extended to evaluate averages over the circular ensemble of unitary matrices. It is then applied to study transport through a disordered metallic ``grain'', attached through ideal leads to a normal electrode and to a superconducting electrode. The latter enforces boundary conditions which coherently couple electrons and holes at the Fermi energy through Andreev scattering. Consequently, the {\it leading order} of the conductance is altered, and thus changes much larger than $e^2/h$ are observed when, e.g., a weak magnetic field is applied. This is in agreement with existing theories. The approach developed here is intermediate between the theory of dirty superconductors (the Usadel equations) and the random-matrix approach involving transmission eigenvalues (e.g. the DMPK equation) in the following sense: even though one starts from a scattering formalism, a quantity analogous to the superconducting order-parameter within the system naturally arises. The method can be applied to a variety of mesoscopic normal-superconducting structures, but for brevity we consider here only the case of a simple disordered N-S junction.Comment: 39 pages + 9 postscript figure

Conductance of Mesoscopic Systems with Magnetic Impurities

We investigate the combined effects of magnetic impurities and applied magnetic field on the interference contribution to the conductance of disordered metals. We show that in a metal with weak spin-orbit interaction, the polarization of impurity spins reduces the rate of electron phase relaxation, thus enhancing the weak localization correction to conductivity. Magnetic field also suppresses thermal fluctuations of magnetic impurities, leading to a recovery of the conductance fluctuations. This recovery occurs regardless the strength of the spin-orbit interaction. We calculate the magnitudes of the weak localization correction and of the mesoscopic conductance fluctuations at an arbitrary level of the spin polarization induced by a magnetic field. Our analytical results for the ``$h/e$'' Aharonov-Bohm conductance oscillations in metal rings can be used to extract spin and gyromagnetic factor of magnetic impurities from existing experimental data.Comment: 18 pages, 8 figure

Nonequilibrium Josephson effect in short-arm diffusive SNS interferometers

We study non-equilibrium Josephson effect and phase-dependent conductance in three-terminal diffusive interferometers with short arms. We consider strong proximity effect and investigate an interplay of dissipative and Josephson currents co-existing within the same proximity region. In junctions with transparent interfaces, the suppression of the Josephson current appears at rather large voltage, $eV\sim \Delta$, and the current vanishes at $eV\geq\Delta$. Josephson current inversion becomes possible in junctions with resistive interfaces, where the inversion occurs within a finite interval of the applied voltage. Due to the presence of considerably large and phase-dependent injection current, the critical current measured in a current biased junction does not coincide with the maximum Josephson current, and remains finite when the true Josephson current is suppressed. The voltage dependence of the conductance shows two pronounced peaks, at the bulk gap energy, and at the proximity gap energy; the phase oscillation of the conductance exhibits qualitatively different form at small voltage $eV<\Delta$, and at large voltage $eV>\Delta$.Comment: 11 pages, 9 figures, revised version, to be published in Phys. Rev.

Thermoelectric effects in superconducting proximity structures

Attaching a superconductor in good contact with a normal metal makes rise to a proximity effect where the superconducting correlations leak into the normal metal. An additional contact close to the first one makes it possible to carry a supercurrent through the metal. Forcing this supercurrent flow along with an additional quasiparticle current from one or many normal-metal reservoirs makes rise to many interesting effects. The supercurrent can be used to tune the local energy distribution function of the electrons. This mechanism also leads to finite thermoelectric effects even in the presence of electron-hole symmetry. Here we review these effects and discuss to which extent the existing observations of thermoelectric effects in metallic samples can be explained through the use of the dirty-limit quasiclassical theory.Comment: 14 pages, 10 figures. 374th WE-Heraus seminar: Spin physics of superconducting heterostructures, Bad Honnef, 200