Anomalous Hall effect in superconductors with spin-orbit interaction

TL;DR

This paper investigates the anomalous Hall conductance in superconductors with spin-orbit interaction, analyzing effects of uniform magnetization and magnetic impurities, revealing oscillations and phase transition indicators.

Contribution

It provides a theoretical analysis of how spin-orbit coupling and magnetization influence the anomalous Hall effect in different types of superconductors, highlighting the use of Hall conductance as a phase transition marker.

Findings

Hall conductance oscillates strongly at high spin-orbit coupling

Hall conductance can track quantum phase transitions

Superconductivity is suppressed at large spin-orbit coupling

Abstract

We calculate the anomalous Hall conductance of superconductors with spin-orbit interaction and with either uniform or local magnetization. In the first case we consider a uniform ferromagnetic ordering in a spin triplet superconductor, while in the second case we consider a conventional s-wave spin singlet superconductor with a magnetic impurity (or a diluted set of magnetic impurities). In the latter case we show that the anomalous Hall conductance can be used to track the quantum phase transition, that occurs when the spin coupling between the impurity and electronic spin density exceeds a certain critical value. In both cases we find that for large spin-orbit coupling the superconductivity is destroyed and the Hall conductance oscillates strongly.