Electric field-induced anisotropic Rashba splitting in two dimensional tungsten dichalcogenides WX2 (X: S, Se, Te): A first-principles study

Tungsten dichalcogenides WX2 (X: S, Se, Te) monolayer (ML) has been considered as important two-dimensional materials for hosting large spin splitting due to the lack of inversion symmetry. However, out-of-plane mirror-symmetry in the WX2 ML suppressed that only out-of-plane Zeeman splitting sustains, thus limiting the functionality for spintronic applications. By using first-principles density-functional theory calculations, we show that application of an external electric field breaks the out-of-plane mirror-symmetry, inducing a sizable Rashba splitting with anisotropic character of spin-polarizations. Our analysis using (k) over right arrow.(p) over right arrow model obtained from the symmetry consideration confirmed that the anisotropic Rashba splitting is mainly originated from contribution of third-order term in the spin-orbit Hamiltonian. Importantly, the Rashba parameter can be effectively modulated by tuning the electric field, giving rise to a maximally field-tunable Rashba splitting. Our study clarify that the electric field plays an important role for controlling the spin splitting in TMDs ML, which is useful for spintronic applications.