"Smile"-gap in the density of states of a cavity between superconductors

TL;DR

This paper predicts a previously overlooked secondary gap in the density of states of a normal metal cavity between superconductors, which varies with phase bias and can be detected experimentally.

Contribution

It introduces the concept of a 'smile'-shaped secondary gap in the density of states of S-N-S structures, expanding understanding of Andreev levels and their phase dependence.

Findings

Secondary gap exists just below the superconducting gap edge.

The secondary gap is widest at zero phase bias and closes at finite bias.

Asymmetric couplings lead to more complex gap structures near phase difference π.

Abstract

The density of Andreev levels in a normal metal ($N$) in contact with two superconductors ($S$) is known to exhibit an induced minigap related to the inverse dwell time. We predict a small secondary gap just below the superconducting gap edge---a feature that has been overlooked so far in numerous studies of the density of states in $S-N-S$ structures. In a generic structure with $N$ being a chaotic cavity, the secondary gap is the widest at zero phase bias. It closes at some finite phase bias, forming the shape of a "smile". Asymmetric couplings give even richer gap structures near the phase difference \pi. All the features found should be amendable to experimental detection in high-resolution low-temperature tunneling spectroscopy.