Linear exciton Hall and Nernst effects in monolayer two-dimensional semiconductors

This paper focuses on the study of linear exciton Hall and Nernst effects in monolayer two-dimensional (2D) semiconductors, employing the semi-classical transport theory. By deriving the exciton Berry curvature in momentum space for a general inhomogeneous 2D system, we establish its dependence on the Berry curvature and the effective mass of electron and hole. As illustrative examples, the exciton Hall effect in monolayer transition metal dichalcogenides (TMDs) and black phosphorus (BP) are calculated. For these materials, we demonstrate that a linear Hall (Nernst) exciton current with the non-zero Berry curvature is strictly forbidden by the symmetries. This finding aligns with earlier experimental observations on the exciton Hall effect in MoSe₂. In contrast, a strong anisotropy in BP leads to a net linear Hall current of excitons, exhibiting a relatively large value and resembling an anomalous Hall effect rather than a valley Hall effect. Our work reveals that the specific symmetry of 2D materials can induce a significant linear exciton Hall (Nernst) effect even without Berry curvature, which is normally forbidden with non-zero Berry curvature in the monolayer 2D material. This observation holds promise for future optoelectronic applications and offers exciting possibilities for experimental exploration.