Nonanalyticity, Valley Quantum Phases, and Light-like Exciton Dispersion in Monolayer TMDs: Theory and First-Principles Calculations

Exciton dispersion as a function of center-of-mass momentum, $\mathbf{\text{Q}}$, 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 MoS${}_2$ and find a nonanalytic light-like dispersion. This behavior arises from an unusual $\mathrm{\mid }Q\mathrm{\mid }$ term in both the intra- and inter-valley 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.