Coupling of electrons to interface phonons in semiconductor quantum wells

In a recent paper [B. K. Ridley and M. Babiker, Phys. Rev. B 43, 9096 (1991)] the authors have arguned that when retardation is taken into account the interface phonons of semiconductor superlattices obtained from the usual dielectric continuum approach are transverse polariton modes and that they therefore do not couple to electrons via the strong Frölich interaction. Here we show that the interface polaritons obtained from this dielectric continuum approach, in general, have both transverse and longitudinal components and that the dispersion and character of the modes are affected by retardation only for small wave vectors (k≲${\mathrm{\omega }}_{\mathrm{phonon}}$/c). For wave vectors of interest in electron-phonon scattering, the interaction is given to a good approximation by the usual Frölich interaction neglecting retardation.