Polar optical phonons in core–shell semiconductor nanowires

•We obtain phonon modes for GaAs–GaP core–shell nanowires within a continuum model.•We report a basis of functions for the space of solutions of the used model.•Inclusion of strain produces an upwards/downwards shift of core/shell modes.

We obtain the long-wavelength polar optical vibrational modes of semiconductor core–shell nanowires by means of a phenomenological continuum model. A basis for the space of solutions is derived, and by applying the appropriate boundary conditions, the transcendental equations for the coupled and uncoupled modes are attained. Our results are applied to the study of the GaAs–GaP core–shell nanowire, for which we calculate numerically the polar optical modes, analyzing the role of strain in the vibrational properties of this nanosystem.