Chiral excitonic systems in twisted bilayers from Förster coupling and unconventional excitonic Hall effects

In twisted bilayer semiconductors with arbitrary twisting angles, a chiral excitonic system can arise from the interlayer electron-hole Coulomb exchange interaction (F\"orster coupling) that hybridizes the anisotropic intralayer excitons from individual layers. We present a general framework for the effective exciton Hamiltonian taking into account the electron-hole Coulomb exchange, using twisted homobilayer systems composed of transition metal dichalcogenides or black phosphorus as examples. We demonstrate that such chiral excitonic systems can feature unconventional Hall (Nernst) effects arising from quantum geometric properties characteristic of the layer hybridized wave functions under the chiral symmetry, for example, the time-reversal even-layer Hall counterflow and the crossed nonlinear dynamical Hall effect, when mechanical and statistical force (temperature or density gradient) drives the exciton flow.