Dispersion, mode-mixing and the electron-phonon interaction in nanostructures

The electron-phonon interaction with polar optical modes in nanostructures is re-examined in the light of phonon dispersion relations and the role of the Fuchs-Kliewer (FK) mode. At an interface between adjacent polar materials the frequencies of the FK mode are drawn from the dielectric constants of the adjacent materials and are significantly smaller than the corresponding frequencies of the longitudinal optic (LO) modes at the zone centre. The requirement that all polar modes satisfy mechanical and electrical boundary conditions forces the modes to become hybrids. For a hybrid to have both FK and LO components the LO mode must have the FK frequency, which can only come about through the reduction associated with phonon dispersion relations. We illustrate the effect of phonon dispersion relations on the Fröhlich interaction by considering a simple linear-chain model of the zincblende lattice. Optical and acoustic modes become mixed towards short wavelengths in both optical and acoustic branches. A study of GaAs, InP and cubic GaN and AlN shows that the polarity of the optical branch and the acousticity of the acoustic branch are reduced by dispersion in equal measures, but the effect is relatively weak. Coupling coefficients quantifying the strengths of the interaction with electrons for optical and acoustic components of mixed modes in the optical branch show that, in most cases, the polar interaction dominates the acoustic interaction, and it is reduced from the long-wavelength result towards the zone boundary by only a few percent. The effect on the lower-frequency FK mode can be large.