Random Matrix Theory of a Chaotic Andreev Quantum Dot

TL;DR

This paper introduces a new universality class for chaotic Andreev quantum dots, characterized by a random-matrix model that accounts for unique spectral and transport properties influenced by superconducting contact and magnetic field effects.

Contribution

It proposes a novel random-matrix framework for a distinct universality class of chaotic Andreev quantum dots with unique spectral and conductance features.

Findings

Identifies a new universality class different from Wigner-Dyson.

Describes a nonzero weak-localization correction to conductance.

Explains depletion of density of states via semiclassical phase-coherent modes.

Abstract

A new universality class distinct from the standard Wigner-Dyson ones is identified. This class is realized by putting a metallic quantum dot in contact with a superconductor, while applying a magnetic field so as to make the pairing field effectively vanish on average. A random-matrix description of the spectral and transport properties of such a quantum dot is proposed. The weak-localization correction to the tunnel conductance is nonzero and results from the depletion of the density of states due to the coupling with the superconductor. Semiclassically, the depletion is caused by a a mode of phase-coherent long-range propagation of electrons and holes.