Effective Random Matrix Theory description of chaotic Andreev billiards

Abstract

An effective random matrix theory description is developed for the universal gap fluctuations and the ensemble averaged density of states of chaotic Andreev billiards for finite Ehrenfest time. It yields a very good agreement with the numerical calculation for Sinai-Andreev billiards. A systematic linear decrease of the mean field gap with increasing Ehrenfest time ${\tau }_E$ is observed but its derivative with respect to ${\tau }_E$ is in between two competing theoretical predictions and close to that of the recent numerical calculations for Andreev map. The exponential tail of the density of states is interpreted semi-classically.

4 pages, 4 figures

References in corpus (3)

• Quantum Andreev map: A paradigm of quantum chaos in superconductivity
• Adiabatic quantization of Andreev levels
• Quasiclassical fluctuations of the superconductor proximity gap in a chaotic system

Cited by in corpus (11)

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• Andreev billiards
• Quantum-to-classical crossover for Andreev billiards in a magnetic field
• Effects of Andreev reflection on the conductance of quantum-chaotic dots
• Superconductivity-induced macroscopic resonant tunneling
• Bound states in Andreev billiards with soft walls
• Quantum-classical correspondence in the wavefunctions of Andreev billiards
• Effect of spin-orbit coupling on the excitation spectrum of Andreev billiards
• Macroscopic Resonant Tunneling through Andreev Interferometers
• Non-universal suppression of the excitation gap in chaotic Andreev billiards: Superconducting terminals as sensitive probes for scarred states
• Quantized invariant tori in Andreev billiards of mixed phase space