Tunable nonlinear anisotropic Rashba splitting in monolayer transition metal dichalcogenide MoS2(1−x)Se2x alloys

We investigate the Rashba effect in thermodynamically stable nonpolar transition metal dichalcogenide (TMD) alloys of the form $\mathrm{Mo}{\mathrm{S}}_{2(1\ensuremath{-}x)}{\mathrm{Se}}_{2x}$ in the presence of an out-of-plane electric field using first-principles calculations. These alloys exhibit a nonlinear anisotropic Rashba effect, which is explained by considering symmetry-dependent higher-order terms in the Rashba Hamiltonian. Of the three stable alloys studied here, $\mathrm{Mo}{\mathrm{S}}_{0.67}{\mathrm{Se}}_{1.33}$ and $\mathrm{Mo}{\mathrm{S}}_{1.33}{\mathrm{Se}}_{0.67}$ belong to the same symmetry group as $\mathrm{Mo}{\mathrm{S}}_{2}$ and $\mathrm{Mo}{\mathrm{Se}}_{2}$, and the anisotropy in their Rashba splitting originates mainly from a single anisotropic third-order term in the Hamiltonian. On the other hand, the MoSSe alloy belongs to the ${C}_{2v}$ point group symmetry, where all the first- and third-order parameters are anisotropic and significantly contribute to the anisotropy of the Rashba effect. Furthermore, the Rashba energy splitting in these nonpolar alloys can be extensively tuned and enhanced significantly by applying a perpendicular external electric field and biaxial strain, making them promising candidates for spintronic applications.