Orbital-related gyrotropic responses in Cu$_2$WSe$_4$ and chirality indicator

Abstract: In recent years, counterparts of phenomena studied in spintronics have been actively explored in the orbital sector. The relationship between orbital degrees of freedom and crystal chirality has also been intensively investigated, although the distinction from gyrotropic properties has not been fully clarified. In this work, we investigate spin and orbital Edelstein effects as well as the nonlinear responses in the ternary transition-metal chalcogenide Cu$_2$WSe$_4$, which has a gyrotropic but achiral crystal structure. We find that in the Edelstein effect, magnetization is dominated by the orbital contribution rather than the spin contribution. On the other hand, both the nonlinear chiral thermoelectric (NCTE) Hall effect--a response to the cross product of the electric field and the temperature gradient--and the nonlinear Hall effect--conventional second-order response to the electric field--are found to be dominated by the Berry curvature dipole. We further find that spin-orbit coupling plays only a minor role in these effects, whereas the orbital degrees of freedom are essential. Finally, we demonstrate that the orbital magnetic-moment contributions to both the Edelstein effect and the NCTE Hall effect are closely linked to chirality, and we discuss the possibility of using them as a chirality indicator.