Trion fine structure and anomalous Hall effect in monolayer transition metal dichalcogenides

We theoretically investigate two spin configurations of a negative trion in monolayer tungstenides, called the intravalley spin singlet and intervalley spin triplet. The energy splitting between them is attributed to the trion fine structure, arising from the electron-hole exchange interaction. Using the Rytova-Keldysh potential, we show that the splitting which acts as an effective Zeeman effect is tuned by varying the dielectric environment. For the negative trion in the ${\mathrm{WSe}}₂$ monolayer encapsulated in hexagonal boron nitride, the calculated splitting is around 6 meV, which is in agreement with recent experiments. Owing to the strong exchange, we show that the negative intervalley trion acquires a giant Berry curvature. This valley pseudospin-dependent Berry curvature largely dominates the intrinsic Berry curvature arising from the Bloch bands. An in-plane applied electric field gives rise to an anomalous valley Hall transport. We investigate the dependence of the anomalous Hall conductivity and magnetization on several parameters such as dielectric screening length and doping. The trion Hall effect can be considered as the basis for valley-based electronics applications.