Random scattering matrices for Andreev quantum dots with nonideal leads

B. Béri

doi:10.1103/PhysRevB.79.214506

← Back to search

Random scattering matrices for Andreev quantum dots with nonideal leads

B. Béri

DOI 10.1103/PhysRevB.79.214506 · Physical Review B

T1

Active bibliographic source — not scientific approval

Bibliographic access preserves source history; it does not approve extracted materials or validate reported claims. Review warnings on each occurrence separately.

Abstract

We calculate the distribution of the scattering matrix at the Fermi level for chaotic normal-superconducting systems for the case of arbitrary coupling of the scattering region to the scattering channels. The derivation is based on the assumption of uniformly distributed scattering matrices at ideal coupling, which holds in the absence of a gap in the quasiparticle excitation spectrum. The resulting distribution is the analog of the Poisson kernel for the nonstandard symmetry classes introduced by Altland and Zirnbauer. We show that unlike the Poisson kernel, the analyticity-ergodicity constraint does not apply to our result. As a simple application, we calculate the distribution of the conductance for a single-channel chaotic Andreev quantum dot in a magnetic field.