Spin Hall effect in two-dimensional InSe: Interplay between Rashba and Dresselhaus spin-orbit couplings

Materials with inversion asymmetries can exhibit strong spin Hall effect (SHE) in the presence of Dresselhaus and Rashba spin-orbit coupling (D/R SOC) interactions. Ideally, in a two-dimensional crystal, inversion asymmetry could be modulated by stacking order and external perturbations. Here, using first-principles calculations, we systematically investigate the interplay between DSOC and RSOC and their influences on SHE in mono- and bilayer InSe. We show that in the presence of DSOC, the introduction of Rashba interaction through gate voltages in monolayer InSe increases Zeeman-like spin splitting around the Brillouin-zone center and contributes to the enhancement of spin Hall conductivity (SHC), which reaches a saturation point due to the RSOC-enforced spiral-spin texture. The SHC in the unperturbed centrosymmetric $\mathit{AB}$ stacked bilayer shows a peak associated with the Mexican-hat-like valence-band edge; however, in a wide energy range the SHC stays insignificant. In the $\mathit{AB}$\ensuremath{'} stacked bilayer with the intrinsic RSOC present, the value of SHC can be comparable to that of $\mathit{AB}$ stacked bilayer with an external electric field. Moreover, we show that the spin-momentum locking in the $\mathit{AB}$\ensuremath{'} stacked bilayer is switchable by a gate voltage. These findings provide a promising route for spintronic and magneto-optical applications by exploiting the rich physics of spin-orbit effects.