  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 $d^* \equiv \epsilon d /
\epsilon_{\text{sol}}$, where $\epsilon$ is the permittivity of the nanosheet
and $\epsilon_{\text{sol}}$ 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 $a_0$ in addition to the length scales $d$ and $d^*$ and analyze the
consequences of this dependence.
