Nonanalyticity, Valley Quantum Phases, and Lightlike Exciton Dispersion in Monolayer Transition Metal Dichalcogenides: Theory and First-Principles Calculations

Exciton dispersion as a function of center-of-mass momentum Q is essential to the understanding of exciton dynamics. We use the ab initio GW-Bethe-Salpeter equation method to calculate the dispersion of excitons in monolayer MoS2 and find a nonanalytic lightlike dispersion. This behavior arises from an unusual vertical bar Q vertical bar-term in both the intra- and intervalley exchange of the electron-hole interaction, which concurrently gives rise to a valley quantum phase of winding number two. A simple effective Hamiltonian to Q(2) order with analytic solutions is derived to describe quantitatively these behaviors.