Non-Hermitian Theory of Valley Excitons in Two-Dimensional Semiconductors

Electron-hole exchange interaction in two-dimensional transition metal dichalcogenides is extremely strong due to the dimension reduction, which promises valley-superposed excitonic states with linearly polarized optical emissions. However, strong circular polarization reflecting valley-polarized excitonic states is commonly observed in helicity-resolved optical experiments. Here, we present a non-Hermitian theory of valley excitons by incorporating optical pumping and intrinsic decay, which unveils an anomalous valley-polarized excitonic state with elliptically polarized optical emission. This novel state arises from the non-Hermiticity induced parity-time (PT) symmetry breaking, which impedes the experimental observation of intervalley excitonic coherence effect. At large excitonic center-of-mass momenta, the PT symmetry is restored and the excitonic states recover their valley coherence. Interestingly, the linear polarization directions in optical emissions from these valley-superposed excitonic states are nonorthogonal and even become parallel at exceptional points. Our non-Hermitian theory also predicts a nonzero Berry curvature for valley excitons, which admits a topological excitonic Hall transport beyond the Hermitian predictions.