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Binding energies of exciton complexes in transition metal dichalcogenides and effect of dielectric environment

Excitons, trions, biexcitons, and exciton-trion complexes in two-dimensional transition metal dichalcogenide sheets of MoS$_2$, MoSe$_2$, MoTe$_2$, WS$_2$ and WSe$_2$ are studied by means of density functional theory and path integral Monte Carlo method in order to accurately account for the particle-particle correlations. In addition, the effect of dielectric environment on the properties of these exciton complexes is studied by modifying the effective interaction potential between particles. Calculated exciton and trion binding energies are consistent with previous experimental and computational studies, and larger systems such as biexciton and exciton-trion complex are found highly stable. Binding energies of biexcitons are similar or higher than those of trions, but the binding energy of the trion depends significantly stronger on the dielectric environment than that of biexciton. Therefore, as a function of an increasing dielectric constant of the environment the exciton-trion complex "dissociates" to a biexciton rather than to an exciton and a trion.