  Recently, it has been demonstrated that the absorption of moderately doped
two-dimensional semiconductors can be described in terms of exciton-polarons.
In this scenario, attractive and repulsive polaron branches are formed due to
interactions between a photo-excited exciton and a Fermi sea of excess charge
carriers. These interactions have previously been treated in a phenomenological
manner. Here, we present a microscopic derivation of the electron-exciton
interactions which utilizes a mixture of variational and perturbative
approaches. We find that the interactions feature classical charge-dipole
behaviour in the long-range limit and that they are only weakly modified for
moderate doping. We apply our theory to the absorption properties and show that
the dependence on doping is well captured by a model with a phenomenological
contact potential.
