Abstract
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^* ≡ ε d / ε_sol, where ε is the permittivity of the nanosheet and ε_sol 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 exciton Bohr radius a₀ in addition to the length scales d and d^* and analyze the consequences of this dependence.