Electric-field-driven exciton vortices in transition metal dichalcogenide monolayers

We predict electric-field-driven exciton vortices in transition metal dichalcogenide monolayers in the BoseEinstein condensation regime. The Rashba spin-orbit coupling created by perpendicular electric fields couples the bright and dark excitons, behaves like an emerging SU(2) gauge field for excitons, and induces spatially asymmetric distribution of exciton density. We find the interplay between the dipole-dipole interaction among excitons and Rashba spin-orbit coupling leads to the phase transitions containing different vortices, from a single pair of vortices to numerous satellite vortices appearing at the edge of the sample. The exciton condensation at the K and K' valleys shows mirror-symmetric patterns composed of exciton vortices rotating oppositely, which are protected topologically by the winding numbers.