Weak Localization Coexisting with a Magnetic Field in a Normal-Metal--Superconductor Microbridge

TL;DR

This paper uses random-matrix theory to show that in a disordered metal-superconductor microbridge, weak localization persists under a magnetic field unless both time-reversal symmetry and electron-hole degeneracy are broken, revealing nuanced quantum effects.

Contribution

It demonstrates that magnetic fields alone do not suppress weak localization in such systems, highlighting the need to break additional symmetries for suppression.

Findings

Weak localization persists with a magnetic field alone.

Suppression requires breaking both time-reversal symmetry and electron-hole degeneracy.

Magnetic-field dependent contact resistance can obscure this effect.

Abstract

A random-matrix theory is presented which shows that breaking time-reversal symmetry by itself does {\em not} suppress the weak-localization correction to the conductance of a disordered metal wire attached to a superconductor. Suppression of weak localization requires applying a magnetic field as well as raising the voltage, to break both time-reversal symmetry and electron-hole degeneracy. A magnetic-field dependent contact resistance obscured this anomaly in previous numerical simulations.