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Background: The Anderson-Bogoliubov (AB) phonon, called also the superfluidphonon, has attracted attentions since it may influence the thermalconductivity and other properties of inner crust of neutron stars. However,there are limited number of microscopic studies of the AB phonon where thepresence of clusters is explicitly taken into account.\\ Purpose: We intend toclarify how the presence of clusters affects the AB phonon in order to obtainmicroscopic information relevant to the coupling between the AB phonon and thelattice phonon. \\ Methods: The Hartree-Fock-Bogoliubov model and thequasiparticle random-phase approximation formulated in a spherical Wigner-Seitzcell are adopted to describe neutron superfluidity and associated collectiveexcitations. We perform systematic numerical calculations for dipole excitationby varying the neutron chemical potential and the number of protons in a cell.\\ Results:The model predicts systematic emergence of the dipole AB phononmode, which however exhibits strong suppression of phonon amplitude inside thecluster. We find also that the phonon amplitude around the cluster surfacevaries as the neutron density. At higher neutron densities the AB phonon modeexhibits behaviour similar to the pygmy dipole resonance in neutron-richnuclei.\\ Conclusions: The dipole AB phonon mode does not penetrate into theclusters. This suggests that the coupling between the AB phonon and the latticephonon may be weak.

Anderson-Bogoliubov phonon in inner crust of neutron stars: Dipole excitation in spherical Wigner-Seitz cell