Large spin-orbit splitting in the conduction band of halogen (F, Cl, Br, and I) doped monolayer WS2 with spin-orbit coupling

Spin-orbit (SO) splitting in the conduction-band minimum (CBM) of monolayer $\mathrm{W}{\mathrm{S}}_{2}$ plays a pivotal role in spintronics for spin-valley coupled electron. Using first-principles calculation, a large SO splitting at the K point in the CBM is achieved in halogen doped monolayer $\mathrm{W}{\mathrm{S}}_{2}$ (83.55 meV for F doped 4 \ifmmode\times\else\texttimes\fi{} 4 \ifmmode\times\else\texttimes\fi{} 1 supercell) because of the strong spin-orbit coupling induced by the asymmetric electric field. We further clarify that the asymmetric electric field originates from the stronger trigonal prismatic ligand field and asymmetric surface charge distribution incurred by halogen doping. More importantly, halogen doping could be used to lift the degeneracy of K and K' valleys in the CBM of monolayer $\mathrm{W}{\mathrm{S}}_{2}$ by breaking the time-reversal symmetry. This research proposes a feasible method to enlarge the SO splitting in the CBM of transition-metal dichalcogenides, advancing their application in valley spintronic devices.