Microscopic theory of the Andreev gap

TL;DR

This paper develops a microscopic theory for the Andreev gap in chaotic cavities attached to superconductors, explaining how quantum fluctuations suppress the density of states at low energies and characterizing the gap profile.

Contribution

It introduces a solution to the quantum Eilenberger equation in the regime where dwell time is much less than Ehrenfest time, providing new insights into the microscopic origin of the Andreev gap.

Findings

Quantum fluctuations eliminate the DoS at low energies.

Computed the gap profile to leading order in the ratio of dwell time to Ehrenfest time.

Established a microscopic framework for understanding the Andreev gap in chaotic systems.

Abstract

We present a microscopic theory of the Andreev gap, i.e. the phenomenon that the density of states (DoS) of normal chaotic cavities attached to superconductors displays a hard gap centered around the Fermi energy. Our approach is based on a solution of the quantum Eilenberger equation in the regime $t_D\ll t_E$, where $t_D$ and $t_E$ are the classical dwell time and Ehrenfest-time, respectively. We show how quantum fluctuations eradicate the DoS at low energies and compute the profile of the gap to leading order in the parameter $t_D/t_E$ .