Phonon-assisted ultrafast dynamics of intra- and inter-layer excitons in 2H and 3R bilayers of MoS₂

We present results for the dynamical properties of excitons that define the emission spectrum of two types (2H and 3R) of laser pulse-excited bilayer (2L) MoS₂, using a combined time-dependent density-functional theory and many-body perturbation theory approach, with a special focus on the role of phonons in the ultrafast response of the systems. Of interest are the characteristics of inter- and intra-layer excitons, which we calculate using our density-matrix TDDFT approach. We find that intra-layer excitons are bound stronger than the inter-layer in both structures (binding energy: 310meV vs. 241meV (2H) and 302meV vs. 190meV (3R)) and that exciton-phonon coupling leads to a significant temperature-dependent renormalization of energies of both types of excitons (for intra-layer excitons at T=4K: 72meV (2H), 78meV (3R)). The formation times for lowest-energy exciton are 0.41ps (2H) and 0.39ps (3R) which are both larger than 0.27ps that find for single layer (1L) MoS₂ and attributed to pronounce intervalley scattering in the 2L case. The exciton radiative lifetimes are also longer in the 2L case, and that in the 3R structure is several times longer than that for the 2H (for T=4K: 4.0ps (1L), 7.2ps (2H), 13.0ps (3R)). We find inter-layer breathing phonon mode responsible for inter-to-intra layer transitions of the excitonic states that are more pronounced in the 3R case. We will discuss the above findings in the light of experimental observation of suppressed inter-layer exciton emission in this structure.