  Background: The Anderson-Bogoliubov (AB) phonon, called also the superfluid
phonon, has attracted attentions since it may influence the thermal
conductivity and other properties of inner crust of neutron stars. However,
there are limited number of microscopic studies of the AB phonon where the
presence of clusters is explicitly taken into account.\\ Purpose: We intend to
clarify how the presence of clusters affects the AB phonon in order to obtain
microscopic information relevant to the coupling between the AB phonon and the
lattice phonon. \\ Methods: The Hartree-Fock-Bogoliubov model and the
quasiparticle random-phase approximation formulated in a spherical Wigner-Seitz
cell are adopted to describe neutron superfluidity and associated collective
excitations. We perform systematic numerical calculations for dipole excitation
by varying the neutron chemical potential and the number of protons in a cell.
\\ Results:The model predicts systematic emergence of the dipole AB phonon
mode, which however exhibits strong suppression of phonon amplitude inside the
cluster. We find also that the phonon amplitude around the cluster surface
varies as the neutron density. At higher neutron densities the AB phonon mode
exhibits behaviour similar to the pygmy dipole resonance in neutron-rich
nuclei.\\ Conclusions: The dipole AB phonon mode does not penetrate into the
clusters. This suggests that the coupling between the AB phonon and the lattice
phonon may be weak.
