Nonlinear optical Hall effect in a Weyl semimetal WTe2

The Hall effect indicates generation of a transverse electric current upon exertion of an longitudinal electric field with an perpendicular magnetic field. While ordinary Hall effect shows linear response with time-reversal symmetry breaking via an applied external magnetic field or their intrinsic magnetization, a nonlinear Hall effect can generically exist in time-reversal symmetric systems resulting from a Berry curvature dipole. Here we report, detections of a nonlinear optical Hall effect in a Weyl semimetal WTe₂ without an external magnetic field at room temperature. The optical Hall effect results in a optical power dependent polarization rotation of the reflected light, called as the nonlinear Kerr rotation. The nonlinear Kerr rotation linearly depends on the charge current density and optical power, which manifests the current-induced third-order Kerr rotation. We quantitatively determine the fourth-order susceptibility, which shows strong anisotropy depending on the directions of the charge current and the light polarization. Moreover, we conduct light energy dependent nonlinear Kerr rotation measurement. We observe strong variation depending on the light energy implying interband transition near 1.5 eV. Employing symmetry analysis of Berry curvature multipoles, we demonstrate that the nonlinear Kerr rotations can arise from the interband Berry curvature multipole allowed by the crystalline symmetries of WTe₂. We also observe the symmetry-forbidden Kerr rotation, which suggest a symmetry lowering during the nonlinear process.