Anomalous Hall effect from a non-Hermitian viewpoint

TL;DR

This paper demonstrates that non-Hermitian effects in equilibrium electronic systems, caused by spin-dependent quasiparticle lifetimes, can induce an anomalous Hall effect without an external magnetic field, revealing a new perspective on quantum transport.

Contribution

It introduces a non-Hermitian effective model for equilibrium systems and links non-Hermiticity to the emergence of the anomalous Hall effect, a novel theoretical insight.

Findings

Non-Hermitian effective models explain anomalous Hall effect in equilibrium.

Spin-dependent quasiparticle lifetimes induce Hall conductivity without magnetic fields.

Calculated conductivities support the non-Hermitian interpretation of quantum transport.

Abstract

Non-Hermitian descriptions often model open or driven systems away from the equilibrium. Nonetheless, in equilibrium electronic systems, a non-Hermitian nature of an effective Hamiltonian manifests itself as unconventional observables such as a bulk Fermi arc and skin effects. We theoretically reveal that spin-dependent quasiparticle lifetimes, which signify the non-Hermiticity of an effective model in the equilibrium, induce the anomalous Hall effect, namely the Hall effect without an external magnetic field. We first examine the effect of nonmagnetic and magnetic impurities and obtain a non-Hermitian effective model. Then, we calculate the Kubo formula from the microscopic model to ascertain a non-Hermitian interpretation of the longitudinal and Hall conductivities. Our results elucidate the vital role of the non-Hermitian equilibrium nature in the quantum transport phenomena.