Dark exciton energy splitting in monolayer WSe2: insights from time-dependent density-functional theory

We present here a formalism based on time-dependent density-functional theory (TDDFT) to describe characteristics of both intra- and inter-valley excitons in semiconductors, the latter of which had remained a challenge. Through the usage of an appropriate exchange-correlation kernel (nanoquanta), we trace the energy difference between the intra- and inter-valley dark excitons in monolayer (1L) WSe2 to the domination of the exchange part in the exchange-correlation energies of these states. Furthermore, our calculated transition contribution maps establish the momentum resolved weights of the electron-hole excitations in both bright and dark excitons thereby providing a comprehensive understanding of excitonic properties of 1L WSe2. We find that the states consist of hybridized excitations around the corresponding valleys which leads to brightening of the dark excitons, i.e., significantly decreasing their lifetime which is reflected in the PL spectrum. Using many-body perturbation theory, we calculate the phonon contribution to the energy bandgap and the linewidths of the excited electrons, holes and (bright) exciton to find that as the temperature increases the bandgap significantly decreases, while the linewidths increase. Our work paves for describing the ultrafast charge dynamics of transition metal dichalcogenide within an ab initio framework.