  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 non-analytic 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 analyse 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.
