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In this work, we theoretically study the nonlinear spin currents in a gatedsingle-layer 1T$'$-WTe$_2$ with strong spin-orbit coupling driven by an intenselaser pulse. We investigate both second and third-order spin currents under theinfluence of an external displacement field. We use an effective low-energyHamiltonian for the modeling and employ Kubo's formalism based on Green'sfunction method. We obtain a large third-order two-color rectified spin Hallcurrent generated by the interference of two co-linear polarised light beamsthat flows transverse to the incident laser polarisation direction. To gain abetter understanding of this phenomenon, we also calculated the second-orderrectified spin current by a single-color light beam and compared it with thetwo-color spin current. To further explore this effect, we analyzed the impactof out-of-plane gate potential, which breaks the inversion symmetry of thesystem and efficiently manipulates the strength and sign of nonlinear spin Hallresponses. As the most striking result of this study, we predict an in-gapnonlinear spin current induced by light without inter-band optical absorption.The in-gap nonlinear charge current is discussed previously, and our findinggeneralizes the effect on the spin channel and third-order response theory.

In-gap Nonlinear Spin Hall Current by Two-color Excitation in Single-layer WTe$_2$