Exchange interaction and polariton effects in quantum-well excitons

We calculate the exchange interaction (EI) of excitons in quantum wells. The EI is found to depend on the in-plane wave vector k, and follows two distinct regimes: for kL≫1, where L is the well width, the EI is enhanced over the bulk value. For kL≪1, the splitting between longitudinal and transverse excitons is linear in k, and vanishes at k=0: thus the common expectation that the longitudinal-transverse splitting increases with confinement is invalid at k=0. Moreover, the exciton polarized along the growth direction is split from the excitons polarized in the planes. The present results yield the dispersion of polariton modes without retardation: for kL≪1, they reduce to those of Nakayama and Matsuura [Surf. Sci. 170, 641 (1986)]. Finally, the dispersion relations of surface polaritons are obtained for all values of kL. Effects due to the interaction with radiation occur at smaller wave vectors than those arising from the EI, so that it is in principle possible to discriminate between the two. Such effects are small in GaAs/${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Al}}_{\mathit{x}}$As quantum wells, where they tend to be hidden by spatial dispersion, but might be observable in materials with smaller exciton radii, as in CuCl. Available experimental data are discussed.