Inheritance of the exciton geometric structure from Bloch electrons in two-dimensional layered semiconductors

We theoretically studied the exciton geometric structure in layered semiconducting transition metal dichalcogenides. Based on a three-orbital tight-binding model for Bloch electrons which incorporates their geometric structures, an effective exciton Hamiltonian is constructed and solved perturbatively to reveal the relation between the exciton and its electron/hole constituent. We show that the electron-hole Coulomb interaction gives rise to a non-trivial inheritance of the exciton geometric structure from Bloch electrons, which manifests as a valley-dependent center-of-mass anomalous Hall velocity of the exciton when two external fields are applied on the electron and hole constituents, respectively. The obtained center-of-mass anomalous velocity is found to exhibit a non-trivial dependence on the fields, as well as the wave function and valley index of the exciton. These findings can serve as a general guide for the field-control of the valley-dependent exciton transport, enabling the design of novel quantum optoelectronic and valleytronic devices.