The Coulomb interaction in two-dimensional semiconductors*

We use a general Coulomb potential form in two-dimensional semiconductor heterostructures and compare the resulting binding energies of neutral and charged excitons in monolayer transition-metal dichalcogenides with those calculated from the Keldysh potential. The results are similar when the dielectric constant of the monolayer is much larger than that of the surrounding layers. The general Coulomb potential form, however, can be used in a wider range of applications in which the Keldysh potential is not a good description (e.g., semiconductors whose thickness is comparable or larger than their Bohr radius), or inadequate (e.g., exciton bound to charged impurities at the substrate). We point to the shortcomings of both potential forms, emphasizing experimental aspects that cannot be reproduced in monolayer transition-metal dichalcogenides. We also discuss an exciton breakup mechanism in which charged impurities at the vicinity of the monolayer dissociate the exciton leading to reduced luminescence efficiency.