Anomalous Hall effect in single-band chiral superconductors from impurity superlattices

TL;DR

This paper explores how impurity superlattices in single-band chiral superconductors can induce an anomalous Hall effect, revealing dependence on superlattice geometry and pairing parity, and showing Hall conductance can appear at the one-loop level.

Contribution

It introduces a novel effective theory for impurity superlattices in chiral superconductors, demonstrating conditions for Hall effect emergence beyond previous models.

Findings

Hall effect depends on superlattice geometry and pairing parity.

Subgap states hybridize into bands enabling Hall conductance.

Hall conductance can appear at the one-loop level due to particle-hole mixing.

Abstract

Unlike anomalous quantum Hall insulators, clean single-band chiral superconductors do not exhibit intrinsic Hall effect at the one-loop approximation. Finite ac Hall conductance was found to emerge beyond one-loop, such as with vertex corrections associated with extrinsic random impurity scatterings. In this paper, we investigate the effect of impurities embedded in single-band chiral superconductors in a superlattice pattern, instead of in random distributions. The impurity-induced Bogoliubov quasiparticle bound states hybridize to form subgap bands, constituting an emergent low-energy effective theory whose Hall effect can be studied with ease. We demonstrate that the occurrence of the Hall effect depends on the superlattice geometry and on the parity of the chiral pairing. In particular, due to the mixed particle-hole character of the subgap states, the Hall conductance may arise at the one-loop level of the current-current correlator in our effective model. Our theory provides a new insight into the impurity-induced anomalous Hall effect in chiral superconductors.