Light-induced charge and spin Hall currents in materials with C4K symmetry

Abstract Berry curvature can manifest itself in current responses. It has recently 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 ) symmetries, while remaining invariant under their combination ( C 4 K ). In this work, we demonstrate that incident light can induce a dc Hall current in such systems. We consider a combination of static and light-induced electric fields. We calculate the current perpendicular to both the static 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 is varied. This allows for rich possibilities such as generating a pure spin current using circularly polarized light. We demonstrate this physics using a two-dimensional toy model with C 4 K symmetry.