A self-consistent scheme for the calculations of the interacting groundstateand the near bandgap optical spectra of mono- and multilayertransition-metal-dichalcogenide systems is presented. The approach combines adielectric model for the Coulomb interaction potential in a multilayerenvironment, gap equations for the renormalized groundstate, and theDirac-Wannier-equation to determine the excitonic properties. To account forthe extension of the individual monolayers perpendicular to their basic plane,an effective thickness parameter in the Coulomb interaction potential isintroduced. Numerical evaluations for the example of MoS$_2$ show that theresulting finite size effects lead to significant modifications in the opticalspectra, reproducing the experimentally observed non hydrogenic features of theexcitonic resonance series. Applying the theory for multi-layer configurations,a consistent description of the near bandgap optical properties is obtained allthe way from monolayer to bulk. In addition to the well-known in-planeexcitons, also interlayer excitons occur in multilayer systems suggesting areinterpretation of experimental results obtained for bulk material.
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