Rigorous Asymptotic Study of the Screened Electrostatic Potential in a Thin Dielectric Slab

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. The Coulomb interaction between a hole and an electron in a thin dielectric slab is computed rigorously by means of a multiple scale expansion. In the 2D limit where the width of the slab is very small with respect to Bohr radius, the effective Hamiltonian is derived. Numerical results for the binding energy of excitons are given for h‐BN and MoS2.