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Time-dependent density-matrix functional theory for trion excitations: application to monolayer MoS2

We study possible optically excited bound states in monolayer MoS2: excitons and trions. For this purpose we formulate and apply a generalized time-dependent density-matrix functional approach for bound states of multiple excitations. The approach was used in the cases of three different types of the exchange-correlation (XC) kernel: 1) two local kernels: a phenomenological contact and the adiabatic local-density approximation (ALDA) (X and XC); 2) gradient-corrected X kernels: GEA, PW91 and PBE; and 3) two long-range (LR) kernels: a phenomenological (Coulomb) and Slater kernels. In the case of exciton, we find that LDA and its gradient-corrected kernels lead to too weak binding energy comparing to the experimental data, while the LR kernels are capable to reproduce the experimental results. Similarly, in the LR case (as well as in the case of local kernel), one can obtain the experimental value of the trion binding energy by taking into account the screening effects. Our results suggest that similar to the excitons, the LR structure of the XC kernel is necessary to describe the trion bound states. Our calculations for the first time confirm theoretically with time-dependent density-functional theory approach that in agreement with experimental data the exciton and trion binding energies are of order of hundreds (excitons) and tenth (trions) meVs, which can be used in different technological applications at the room temperature regime. The approach can be straightforwardly extended on the case of bound states and nonequilibrium response of systems with larger number of bound electrons and holes, including biexcitons.