Diagrammatic theory of random scattering matrices for normal-metal{endash}superconducting mesoscopic junctions
- Institute for Theoretical Physics, University of California, Santa Barbara, California 93106 (United States)
The planar-diagrammatic technique of large-{ital 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 {open_quote}{open_quote}grain{close_quote}{close_quote} 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 {ital leading} {ital order} of the conductance is altered, and thus changes much larger than {ital e}{sup 2}/{ital 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 Dorokhov-Mello-Pereyra-Kumar 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-metal{endash}superconducting ({ital N}-{ital S}) structures, but for brevity we consider here only the case of a simple disordered {ital N}-{ital S} junction. {copyright} {ital 1996 The American Physical Society.}
- OSTI ID:
- 383188
- Journal Information:
- Physical Review, B: Condensed Matter, Journal Name: Physical Review, B: Condensed Matter Journal Issue: 10 Vol. 54; ISSN PRBMDO; ISSN 0163-1829
- Country of Publication:
- United States
- Language:
- English
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