# Anisotropic Keldysh interaction

## TL;DR

This paper extends the classical models of Coulomb interaction in thin films to anisotropic materials, providing analytical expressions for weak anisotropy and highlighting unresolved challenges in strong anisotropy cases.

## Contribution

It generalizes the Rytova-Keldysh model to anisotropic permittivity, deriving explicit formulas for weak anisotropy and identifying open problems for strong anisotropy.

## Key findings

- Explicit asymptotic expressions for weak anisotropy
- Analytical form of electrostatic potential energy
- Unresolved inverse Fourier transform for strong anisotropy

## Abstract

We generalize the classic calculations by Rytova and Keldysh of screened Coulomb interaction in semiconductor thin films to systems with anisotropic permittivity tensor. Explicit asymptotic expressions for electrostatic potential energy of interaction in the weakly anisotropic case are found in closed analytical form. The case of strong in-plane anisotropy, however, requires evaluation of the inverse Fourier transform of $1/(k+Ak_x^2+Bk_y^2)$, which, at present, remains unresolved.