  We investigate the influence of the one-dimensional character of the phonon
modes in a catalytically grown GaAs nanowire on the absorption spectrum of an
embedded quantum dot, focusing on the contribution from the piezoelectric
coupling. In general, the reduced dimensionality of the phonons leads to
spectral side peaks and a zero-phonon line broadening due to the energetically
lowest (acoustic) phonon mode. While the deformation potential predominantly
couples to radial modes, the piezoelectric interaction can also couple strongly
to modes of axial character, leading to additional absorption features. The
contribution of the piezoelectric coupling to the zero-phonon line is
negligible.
