We settle a general expression for the Hamiltonian of the electron-phonon deformation potential (DP) interaction in the case of non-polar core-shell cylindrical nanowires (NWs). On the basis of long range phenomenological continuum model for the opti
cal modes and by taking into account the bulk phonon dispersions, we study the size dependence and strain-induced shift of the electron-phonon coupling strengths for Ge-Si and Si-Ge NWs. We derive analytically the DP electron-phonon Hamiltonian and report some numerical results for the frequency core modes and vibrational amplitudes. Our approach allows for the unambiguous identification of the strain and confinement effects. We explore the dependence of mode frequencies and hole-DP scattering rates on the structural parameters of these core-shell structures, which constitute a basic tool for the characterization and device applications of these novel nanosystems.
