Effect of spin-orbit coupling on the excitation spectrum of Andreev billiards

TL;DR

This paper investigates how spin-orbit coupling influences the low-energy excitation spectrum of Andreev billiards, revealing effects like gap narrowing, oscillations, and zero-energy peaks consistent with random-matrix theory predictions.

Contribution

It introduces a dynamical numerical model to study spin-orbit effects on Andreev billiards, confirming three predicted phenomena through simulations.

Findings

Narrowing of excitation gap distribution at zero magnetic field

Oscillations in the average density of states due to spin-orbit coupling

Zero-energy peak in the density of states under strong magnetic field

Abstract

We consider the effect of spin-orbit coupling on the low energy excitation spectrum of an Andreev billiard (a quantum dot weakly coupled to a superconductor), using a dynamical numerical model (the spin Andreev map). Three effects of spin-orbit coupling are obtained in our simulations: In zero magnetic field: (1) the narrowing of the distribution of the excitation gap; (2) the appearance of oscillations in the average density of states. In strong magnetic field: (3) the appearance of a peak in the average density of states at zero energy. All three effects have been predicted by random-matrix theory.