General explicit analytical expressions for the charge-charge interaction energy $W(Z,Z^{\prime },R)$ between two point charges in heterostructures with three plane layers were obtained in the framework of classical electrostatics, i.e., the dielectric permittivities of the constituent media were assumed to be constant. Here, $R$ is the lateral (along the interfaces) distance between the charges, and $Z$ and $Z^{\prime }$ are their normal coordinates. The obtained results may be applied to the interaction between charges for their various arrangements in the layered system. For instance, the interaction across the interlayer was calculated as the function of the dielectric constants ${\varepsilon }_i(i=1,2,3)$ of the constituent media. It was demonstrated that the textbook Coulomb expression is far from being valid in this case. In particular, more sophisticated formulas proposed here should be used when considering interlayer excitons in heterostructures of various kinds and electron-hole superfluidity in such sandwiches.

• Received 10 January 2022
• Revised 24 February 2022
• Accepted 2 March 2022

DOI:https://doi.org/10.1103/PhysRevB.105.115415