Exchange-enhanced spin-orbit splitting and its density dependence in monolayer transition metal dichalcogenides

We show that spin-orbit splitting (SOS), which leads to the spin-valley locking in monolayers of semiconducting transition metal dichalcogenides (TMDs), is substantially enhanced by electron-electron interaction. This enhancement, similar to the exchange-driven increase of the electron g-factor, is particularly pronounced for conduction-band electrons, especially in MoS₂, and exhibits a non-monotonic dependence on the carrier sheet density, n. Notably, SOS reaches a maximum at a critical density n_* at the onset of filling of the higher-energy spin-split band by electrons, n_* This threshold density n_* separates the regimes of slow (at n< n_*) and fast (for n>n_*) spin and valley relaxation of charge carriers. Moreover, this density itself is determined by the enhanced SOS value, making the account of exchange renormalisation important for the analysis of spintronic performance of field-effect transistors based on two-dimensional TMDs. This finding highlights the intricate link between SOS, carrier density, and relaxation regimes, which is essential for optimizing spintronic applications of TMDs.