Emergent Spin Hall phase at a Lifshitz transition from competing orders

TL;DR

This paper explores how competing orders like superconductivity and ferromagnetism influence a 2D Rashba semimetal, revealing a new spin Hall phase and anomalous Hall effect linked to Lifshitz transitions and Berry curvature effects.

Contribution

It uncovers a novel intrinsic anomalous Hall effect and emergent spin Hall phase in a Rashba semimetal due to competing orders, with implications for topological phase transitions.

Findings

Discovery of a robust intrinsic AHE from Berry curvature effects.

Identification of an emergent spin Hall phase at a Lifshitz transition.

Coexistence of multiple Hall effects despite disorder.

Abstract

The effects of competing orders, such as superconductivity and ferromagnetism, on a Fermi liquid are well established. A comprehensive understanding of such a competition in a metal whose Fermi surface has a non-trivial topology is yet to be achieved. Here, we address this question in a prototypical system: the 2D Rashba semimetal. We show that dominant superconductivity interplays with Rashba spin orbit interactions (SOI) in forming a novel intrinsic anomalous Hall effect (AHE) with gapless edge states of Bogoliubov-de Gennes (BdG) quasiparticles. As in the case of itinerant ferromagnets, the intrinsic AHE arises from Berry curvature effects in the band structure. This phenomenon is robust even as sub-dominant ferromagnetism dramatically changes the nature of pairing symmetry. An emergent spin Hall phase involving a change in Fermi-surface topology is found to accompany this Lifshitz quantum phase transition. We demonstrate the coexistence of the original and novel AHE in the presence of weak disorder. We offer a comparison of our results with experiments on the two dimensional electron gas at oxide hetero-interfaces as well as make some testable predictions.