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Excitons in van der Waals heterostructures: The important role of dielectric screening

The existence of strongly bound excitons is one of the hallmarks of the newly discovered atomically thin semi-conductors. While it is understood that the large binding energy is mainly due to the weak dielectric screening in two dimensions (2D), a systematic investigation of the role of screening on 2D excitons is still lacking. Here we provide a critical assessment of a widely used 2D hydrogenic exciton model which assumes a dielectric function of the form ε(q) = 1 + 2παq, and we develop a quasi-2D model with a much broader applicability. Within the quasi-2D picture, electrons and holes are described as in-plane point charges with a finite extension in the perpendicular direction and their interaction is screened by a dielectric function with a non-linear q-dependence which is computed ab-initio. The screened interaction is used in a generalized Mott-Wannier model to calculate exciton binding energies in both isolated and supported 2D materials. For isolated 2D materials, the quasi-2D treatment yields results almost identical to those of the strict 2D model and both are in good agreement with ab-initio many-body calculations. On the other hand, for more complex structures such as supported layers or layers embedded in a van der Waals heterostructure, the size of the exciton in reciprocal space extends well beyond the linear regime of the dielectric function and a quasi-2D description has to replace the 2D one. Our methodology has the merit of providing a seamless connection between the strict 2D limit of isolated monolayer materials and the more bulk-like screening characteristics of supported 2D materials or van der Waals heterostructures.