7 research outputs found
A Diagrammatic Theory of Random Scattering Matrices for Normal-Superconducting Mesoscopic Junctions
The planar-diagrammatic technique of large- 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
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