Manipulation of the large Rashba spin splitting in polar two-dimensional transition-metal dichalcogenides

Transition-metal dichalcogenide (TMD) monolayers $MXY\phantom{\rule{0.16em}{0ex}}(M=\mathrm{Mo},\phantom{\rule{0.16em}{0ex}}\mathrm{W};X\phantom{\rule{0.16em}{0ex}}\ensuremath{\ne}\phantom{\rule{0.16em}{0ex}}Y=\mathrm{S},\phantom{\rule{0.16em}{0ex}}\mathrm{Se},\phantom{\rule{0.16em}{0ex}}\mathrm{Te})$ are two-dimensional polar semiconductors. Setting the WSeTe monolayer as an example and using density functional theory calculations, we investigate the manipulation of Rashba spin-orbit coupling (SOC) in the MXY monolayer. It is found that the intrinsic out-of-plane electric field due to the mirror symmetry breaking induces the large Rashba spin splitting around the $\mathrm{\ensuremath{\Gamma}}$ point, which, however, can be easily tuned by applying the in-plane biaxial strain. Through a relatively small strain (from $\ensuremath{-}2%$ to 2%), a large tunability (from around $\ensuremath{-}50%$ to 50%) of Rashba SOC can be obtained due to the modified orbital overlap, which can in turn modulate the intrinsic electric field. The orbital selective external potential method further confirms the significance of the orbital overlap between $\mathrm{W}\text{\ensuremath{-}}{d}_{{z}^{2}}$ and $\mathrm{Se}\text{\ensuremath{-}}{p}_{z}$ in Rashba SOC. In addition, we also explore the influence of the external electric field on Rashba SOC in the WSeTe monolayer, which is less effective than strain. By calculating the electric-field-induced Rashba SOC in all six $M{X}_{2}$ monolayers, the rule of the electric-field influence on Rashba SOC in TMD monolayers is demonstrated. The large Rashba spin splitting, together with the valley spin splitting in MXY monolayers, may make a special contribution to semiconductor spintronics and valleytronics.