  We theoretically investigate the scenario of a semiconductor quantum well in
a microcavity, where the band structure is arranged such that optically excited
electron-hole pairs cannot form Coulomb-bound excitonic states. However, it is
still possible to form exciton polaritons (part-light, part-matter
quasiparticles), where the excitons are bound via the exchange of microcavity
photons rather than via Coulomb interactions. Using a diagrammatic theory, we
determine the spectral response of the semiconductor microcavity, which
includes exciton-polariton resonances as well as a continuum of unbound
electron-hole pairs. Our method also gives us access to the photon fraction and
the electron-hole wave function of the exciton polariton. In particular, we
obtain the conditions under which an exciton is bound by photon exchange and we
show that Coulomb interactions can enhance binding at large cavity photon
frequencies. Our results for the spectral response are in good agreement with a
recent experiment on doped quantum wells [E. Cortese et al., Nat. Phys. 17, 31
(2021)].
