  A theoretical model for excitons confined in layered metal halide perovskites
is presented. The model accounts for polaronic effects, dielectric and quantum
confinement by means of effective mass theory, image charges and Haken
potentials. We use it to describe the band edge exciton of MAPbI$_3$ structures
surrounded by organic ligands. It is shown that the quasi-2D quantum and
dielectric confinement of layered perovskites squeezes the exciton radius, and
this in turn enhances polaronic effects as compared to 3D structures. The
strong polaronic effects boost the binding energies and radiative recombination
probabilities, which allows one to match experimental data in related systems.
The thickness dependence of Coulomb polarization and self-energy potentials is
in fair agreement with sophisticated atomistic models.
