Theory of anomalous Hall effect from screened vortex charge in a phase disordered superconductor

TL;DR

This paper investigates how vortex charges and their screening influence the anomalous Hall effect in phase-disordered superconductors, revealing a connection between normal and superconducting Hall responses through vortex dynamics and screening effects.

Contribution

It introduces a gauge-invariant framework showing how vortex charge screening affects the Hall response in phase-disordered superconductors, linking normal and superconducting Hall conductivities.

Findings

Vortex and antivortex charge difference is determined by Fermi surface Berry phase.

Screening of vortex charge occurs due to interactions, with a delayed reappearance in the longitudinal current.

The dc Hall conductivity aligns with the ac Hall conductance, not the screened vortex charge.

Abstract

Motivated by recent experiments showing evidence for chiral superconductivity in an anomalous Hall phase of tetralayer graphene, we study the relation between the normal state anomalous Hall conductivity and that in the phase disordered state above the critical temperature of the superconductor. By a numerical calculation of superconductivity in an anomalous Hall metal, we find that a difference in vortex and antivortex charge is determined by the Fermi surface Berry phase. Combining this with the vortex dynamics in a back-ground supercurrent leads to a Hall response in the phase disordered state of the superconductor that is close to the normal state anomalous Hall response. However, using a gauge-invariant superconducting response framework, we find that while vortex charge is screened by interactions, the screening charge, after a time-delay, reappears in the longitudinal current. Thus, the dc Hall conductivity in this phase, instead of matching the screened vortex charge, matches the ac Hall conductance in the superconducting and normal phase, which are similar.