Light-induced charge and spin Hall currents in materials with $C_4K$ symmetry

TL;DR

This paper predicts that light can induce a dc charge and spin Hall current in materials with $C_4K$ symmetry through Berry curvature quadrupole effects, enabling control of spin and charge currents via light polarization.

Contribution

It introduces a mechanism for light-induced dc Hall currents driven by Berry curvature quadrupoles in $C_4K$ symmetric materials, highlighting spin polarization and polarization-dependent effects.

Findings

Light induces dc charge and spin Hall currents in $C_4K$ symmetric systems.

The induced charge current depends on light polarization, while the spin current does not.

Circularly polarized light can generate spin currents in altermagnetic materials.

Abstract

Berry curvature, a momentum space property, can manifest itself in current responses. The well-known anomalous Hall effect in time-reversal-breaking systems arises from a Berry curvature monopole. In time-reversal-invariant materials, a second-order Hall conductivity emerges from a Berry curvature dipole. Recently, it has been shown that a Berry curvature quadrupole induces a third-order ac Hall response in systems that break time reversal ($K$) and a fourfold rotational ($C_{4}$) symmetry, while remaining invariant under the combination of the two ($C_{4}K$). In this letter, we demonstrate that incident light can induce a $\rm dc$ Hall current in such systems, driven by the Berry curvature quadrupole. We consider a combination of a static $\rm dc$ electric field and an ac light-induced electric field. We calculate the current perpendicular to both the static electric field and the fourfold axis. Remarkably, the induced current is generically spin-polarized. A net charge current appears for light that is linearly or elliptically polarized, but not for circular polarization. In contrast, the spin current remains unchanged when the polarization of light is varied. This allows for rich possibilities such as generating a spin current by shining circularly polarized light on an altermagnetic material. We demonstrate this physics using a two-dimensional toy model for altermagnets.