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We study possible optically excited bound states in monolayer MoS2: excitonsand trions. For this purpose we formulate and apply a generalizedtime-dependent density-matrix functional approach for bound states of multipleexcitations. The approach was used in the cases of three different types of theexchange-correlation (XC) kernel: 1) two local kernels: a phenomenologicalcontact 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 ofexciton, we find that LDA and its gradient-corrected kernels lead to too weakbinding energy comparing to the experimental data, while the LR kernels arecapable to reproduce the experimental results. Similarly, in the LR case (aswell as in the case of local kernel), one can obtain the experimental value ofthe trion binding energy by taking into account the screening effects. Ourresults suggest that similar to the excitons, the LR structure of the XC kernelis necessary to describe the trion bound states. Our calculations for the firsttime confirm theoretically with time-dependent density-functional theoryapproach that in agreement with experimental data the exciton and trion bindingenergies are of order of hundreds (excitons) and tenth (trions) meVs, which canbe used in different technological applications at the room temperature regime.The approach can be straightforwardly extended on the case of bound states andnonequilibrium response of systems with larger number of bound electrons andholes, including biexcitons.

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