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

Abstract

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.

39 pages + 9 postscript figures

References in corpus (9)

• Universal Quantum Signatures of Chaos in Ballistic Transport
• Random Matrix Theory of a Chaotic Andreev Quantum Dot
• Scaling Theory of Conduction Through a Normal-Superconductor Microbridge
• Giant Backscattering Peak in Angle-Resolved Andreev Reflection
• Magnetoconductance of ballistic chaotic quantum dots: A Brownian motion approach for the $S$-matrix
• Weak Localization Coexisting with a Magnetic Field in a Normal-Metal--Superconductor Microbridge
• Crossover Driven by Time-reversal Symmetry Breaking in Quantum Chaos
• Quantum interference and the spin orbit interaction in mesoscopic normal-superconducting junctions
• Exactly Solvable Scaling Theory of Conduction in Disordered Wires

Cited by in corpus (8)

• Random-Matrix Theory of Quantum Transport
• Phase coherent transport in hybrid superconducting nanostructures
• Andreev Conductance of Chaotic and Integrable Quantum Dots
• Reflection of light from a disordered medium backed by a phase-conjugating mirror
• Finite Dimensional Statistical Inference
• Random Scattering Matrices and the Circuit Theory of Andreev Conductances
• Many-body systems with random spatially local interactions
• Effective field theory of random quantum circuits