Title: Mapping of the dark exciton landscape in transition metal dichalcogenides,
Abstract: Transition metal dichalcogenides (TMDs) exhibit a remarkable exciton physics
including optically accessible (bright) as well as spin- and momentum-forbidden
(dark) excitonic states. So far the dark exciton landscape has not been
revealed leaving in particular the spectral position of momentum-forbidden dark
states completely unclear. This has a significant impact on the technological
application potential of TMDs, since the nature of the energetically lowest
state determines, if the material is a direct-gap semiconductor. Here, we show
how dark states can be experimentally revealed by probing the intra-excitonic
1s-2p transition. Distinguishing the optical response shortly after the
excitation (< 100$\,$fs) and after the exciton thermalization (> 1$\,$ps)
allows us to demonstrate the relative position of bright and dark excitons. We
find both in theory and experiment a clear blue-shift in the optical response
demonstrating for the first time the transition of bright exciton populations
into lower lying momentum- and spin-forbidden dark excitonic states in
monolayer WSe$_2$.