Nontrivial twisted bilayer chiral excitonic systems: F\"{o}rster coupling and related Hall effect

In bilayers composed of monolayers of two-dimensional semiconductors with arbitrary twisting angles, an effective excitonic system can be established based on the valley excitons of each layer. Instead of direct interlayer hopping, a pronounced F\"{o}rster coupling connects intralayer excitons in different layers, which modifies the energy of the monolayer excitonic system. Surprisingly, two new types of Hall effect recently discovered in electric systems-the time-reversal even charge Hall effect (TREHE) and the crossed nonlinear dynamical Hall effect (CNDHE)-can occur in these systems due to the chiral structure induced by the twist of two layers. We illustrate this point by employing a general theoretical framework to establish the effective excitonic Hamiltonians in twisted homo-bilayer systems composed of transition metal dichalcogenides (TMD) and black phosphorus (BP), calculating the Hall effect in these systems as examples. Regarding the TREHE, our calculations show that it depends on the anisotropy of excitons, resulting in a negligible Hall conductivity for TMD without strain due to the isotropic excitons, but a large Hall conductivity for TMD with chiral symmetric excitons induced by strain. Meanwhile, BP exhibits a finite Hall conductivity due to its high anisotropy. As for the CNDHE, only the specific value of twisted angles can induce a significant Hall conductivity in BP and TMD with strain. This work uncovers nontrivial physical properties of twisted bilayer chiral excitonic systems and provides new opportunities for valley exciton optoelectronics in the layer degree of freedom.