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 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 AB' stacked bilayer with the intrinsic RSOC present, the value of SHC can be comparable to that of AB stacked bilayer with an external electric field. Moreover, we show that the spin-momentum locking in the AB' 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.