# Rigorous asymptotic study of the screened electrostatic potential in a thin dielectric slab

## TL;DR

This paper rigorously analyzes the asymptotic behavior of the screened electrostatic potential in ultra-thin dielectric slabs, deriving exact effective 2D potentials to aid exciton energy calculations in 2D materials.

## Contribution

It provides a rigorous asymptotic analysis and explicit expressions for the screened Coulomb potential in thin dielectric slabs, advancing theoretical understanding for 2D material exciton studies.

## Key findings

- Derived regularized expressions for the potential.
- Obtained exact effective 2D potential formulas.
- Facilitates accurate exciton binding energy computations.

## Abstract

The screened Coulomb potential plays a crucial role in the binding energies of excitons in a thin dielectric slab. The asymptotic behavior of this potential is studied when the thickness of the slab is very small as compared to the exciton Bohr radius. A regularized expression is given and the exact effective 2D potential is derived. These expressions may be useful for the computation of the exciton binding energy in 2D or quasi-2D materials.