Optical emission from light-like and particle-like excitons in monolayer transition metal dichalcogenides

Several monolayer transition metal dichalcogenides (TMDs) are direct band gap semiconductors and potentially efficient emitters in light emitting devices. Photons are emitted when strongly bound excitons decay radiatively, and accurate models of such excitons are important for a full understanding of the emission. Importantly, photons are emitted in directions uniquely determined by the exciton center of mass momentum and with lifetimes determined by the exciton transition matrix element. The exciton band structures of two-dimensional hexagonal materials, including TMDs, are highly unusual with coexisting particle- and light-like bands. The latter is nonanalytic with emission selection rules essentially opposite to the particle-like states, but has been ignored in analyses of TMD light emission so far. In the present work, we analyze the temperature and angular dependence of light emission from both exciton species and point out several important consequences of the unique exciton band structure. Within a first-principles density-functional-theory+Bethe-Salpeter-equation framework, we compute exciton band structures and optical matrix elements for the important TMDs MoS2, MoSe2, WS2, and WSe2. At low temperature, only the particle-like band is populated and our results agree with previous work. However, at slightly elevated temperatures, a significant population of the light-like band leads to modified angular emission patterns and lifetimes. Clear experimental fingerprints are predicted and explained by a simple four-state model incorporating spin-orbit as well as intervalley exchange coupling.