Exciton-phonon and electron-phonon interactions in monolayer and bilayer WSe₂

We present results for phonon-renormalized spectral properties of electrons, holes and excitons in monolayer (1L) and bilayer (2L) WSe₂, which are respectively direct and indirect bandgap semiconductors. Using a combination of time-dependent density-functional theory and second-order many-body perturbation theory, we find that the electron-phonon couplings are dominated by acoustic modes and lead to similar temperature dependencies of the electron and hole spectra for both materials, with an average coupling constant of ~0.1. On the other hand, because of different momentum and spatial structures of excitons, phonons affect excitons in the two systems differently. The binding energy of excitons in 1L is strengthened by 40meV, while that of the intra-layer excitons in the 2L WSe₂ changes by 21meV. There is a significant difference in the exciton-phonon (X-ph) coupling in 1L and 2L WSe₂ – while optical phonon-coupling dominates in the 1L case, for 2L we find a large contribution of the acoustic modes to the X-ph coupling. For inter-layer excitons in 2L, we found a significant phonon-induced modification of their energy (18meV) resulting from the interaction with inter-layer optical phonon modes. This interaction, in addition to lowering the exciton energy, facilitates transformation (transfer) of the inter-layer excitons into intra-layer excitonic states. Our results may help to better understand the role of phonons in the electronic and excitonic properties of 2D transition metal dichalcogenides.