Effects of material thickness and surrounding dielectric medium on Coulomb interactions and two-dimensional excitons

We examine the impact of quantum confinement on the interaction potential between two charges in two-dimensional semiconductor nanosheets in solution. The resulting effective potential depends on two length scales, namely, the thickness d and an emergent length scale d∗ϵd/ϵsol, where ϵ is the permittivity of the nanosheet and ϵsol is the permittivity of the solvent. In particular, quantum confinement, and not electrostatics, is responsible for the logarithmic behavior of the effective potential for separations smaller than d, instead of the one-over-distance bulk Coulomb interaction. Finally, we corroborate that the exciton binding energy also depends on the two-dimensional Bohr radius a0 in addition to the length scales d and d∗ and analyze the consequences of this dependence.