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General expressions for the electron- and hole-acoustical-phonon deformationpotential Hamiltonian (H_{E-DP}) are derived for the case of Ge/Si and Si/Gecore/shell nanowire structures (NWs) with circular cross section. Based on theshort-range elastic continuum approach and on derived analytical results, thespatial confined effects on the vector phonon displacement, the phonondispersion relation and the electron- and hole-phonon scattering amplitudes areanalyzed. It is shown that the acoustical vector displacement, phononfrequencies and H_{E-DP} present mixed torsional, axial, and radial componentsdepending on the angular momentum quantum number and phonon wavector underconsideration. The treatment shows that bulk group velocities of theconstituent materials are renormalized due to the spatial confinement andintrinsic strain at the interface. The role of insulating shell on the phonondispersion and electron-phonon coupling in Ge/Si and Si/Ge NWs are discussed.

Electron-acoustic-phonon interaction in core/shell Ge/Si and Si/Ge nanowires