Layer degree of freedom for excitons in transition metal dichalcogenides

Layered transition metal dichalcogenides (TMDCs) host a variety of strongly bound exciton complexes that control the optical properties in these materials. Apart from spin and valley, layer index provides an additional degree of freedom in a few-layer-thick film. Here we show that in a few-layer TMDC film, the wave functions of the conduction and valence-band-edge states contributing to the K (K') valley are spatially confined in the alternate layers-giving rise to direct (quasi-)intralayer bright exciton and lower-energy interlayer dark excitons. Depending on the spin and valley configuration, the bright-exciton state is further found to be a coherent superposition of two layer-induced states, one (E type) distributed in the even layers and the other (O type) in the odd layers. The intralayer nature of the bright exciton manifests as a relatively weak dependence of the exciton binding energy on the thickness of the few-layer film, and the binding energy is maintained up to 50 meV in the bulk limit-which is an order of magnitude higher than conventional semiconductors. Fast Stokes energy transfer from the intralayer bright state to the interlayer dark states provides a clear signature in the layer-dependent broadening of the photoluminescence peak, and plays a key role in the suppression of the photoluminescence intensity observed in TMDCs with thickness beyond a monolayer.