MX family: an efficient platform for topological spintronics based on Rashba and Zeeman-like spin splittings

Taking various combinations of M = (Mo, W) and X = (C, S, Se) as examples, we propose that MX (M = transition metals, X = IV,V or VI elements) family can establish an excellent platform for both conventional and topological spintronics applications based on anisotropic Rashba-like and non-magnetic Zeeman-type spin splittings with electrically tunable nature. In particular, we observe sizeable Zeeman-like and Rashba-like spin splittings with an anisotropic nature. Meanwhile, they exhibit Rashba-like and topologically robust helical edge states when grown in ferroelectric and paraelectric phases, respectively. These MX monolayers are realized to be quantum valley Hall insulators due to valley contrasting Berry curvatures. The carriers in these MX monolayers can be selectively excited from opposite valleys depending on the polarity of circularly polarized light. The amplitude of the spin splitting can be further tuned by applying external means such as strain, electric field or alloy engineering. Furthermore, considering graphene sheet over the WC monolayer as a prototype example, we show that these MX monolayers can boost the relativistic effect by coupling with the systems exhibiting extremely weak spin-orbit coupling (SOC). Depending on the surface of WC monolayer in contact with the graphene sheet, graphene over WC monolayer passes through the transformation from the semiconducting junction to the Shotcky barrier-free contact. Finally, we reveal that these MX monolayers could also be grown on the substrates such as WS2(001)and GaTe (001) with type-II band alignment, where electron and hole become layer splitted across the interface. Our analysis should be fairly applied to other systems with strong SOC and an equivalent geometrical structure to the MX monolayers.