Polaronic states in a slab of a polar crystal

The ground state and the first excited state of the polaron confined in a slab of a polar crystal are investigated. Both the bulk longitudinal-optical and the surface optical (SO) modes are included in our consideration of the electron-phonon interaction. The polaron self-energy due to either mode of phonon is calculated as a function of the thickness of the slab. It is found that the SO-phonon contribution changes the behavior of the polaron self-energy qualitatively. Instead of monotonically increasing with the slab thickness it increases to a maximum at the beginning and then decreases to the bulk value as its limit when the thickness increases indefinitely. A number of other interesting features are also discussed.