In-gap Nonlinear Spin Hall Current by Two-color Excitation in Single-layer WTe2

In this work, we theoretically study the nonlinear spin currents in a gated single-layer 1T′-WTe2 with strong spin-orbit coupling driven by an intense laser pulse. We investigate both second and third-order spin currents under the influence of an external displacement field. We use an effective low-energy Hamiltonian for the modeling and employ Kubo's formalism based on Green's function method. We obtain a large third-order two-color rectified spin Hall current generated by the interference of two co-linear polarised light beams that flows transverse to the incident laser polarisation direction. To gain a better understanding of this phenomenon, we also calculated the second-order rectified spin current by a single-color light beam and compared it with the two-color spin current. To further explore this effect, we analyzed the impact of out-of-plane gate potential, which breaks the inversion symmetry of the system and efficiently manipulates the strength and sign of nonlinear spin Hall responses. As the most striking result of this study, we predict an in-gap nonlinear spin current induced by light without inter-band optical absorption. The in-gap nonlinear charge current is discussed previously, and our finding generalizes the effect on the spin channel and third-order response theory.