Electron-phonon interaction in a dielectric slab: Effect of the electronic polarizability

Abstract

The operators describing the interaction between an electron and the phonon modes of an ionic crystal slab (the bulklike sinusoidal modes and the localized surface modes) are calculated with the proper inclusion of the electronic polarizability. Since the effect of the electronic polarizability on the interaction operators exhibits itself through the amplitudes of the polarization eigenvectors, we must first derive the eigenvectors, eigenfrequencies, and amplitudes of the various phonon modes. We show that the electron-LO-phonon operator derived here is equivalent, for a very thick slab, to the Fröhlich operator for bulk LO phonons, and that the electron-surface-phonon interaction operator leads to the classical image-charge theory result for the interaction energy of an electron external to a semi-infinite crystal and the polarization eigenmodes of the crystal.