Special Phonons and Superconductivity in the Hexagonal Tungsten Bronzes

Neutron scattering measurements on single crystals of hexagonal tungsten bronzes $M_{0.33}$ W${\mathrm{O}}_3$ reveal low-frequency, relatively dispersionless phonon branches which can be associated with the vibrations of the metal atoms $M$ in the large open channels they occupy in the crystal structure. An analysis based on Eliashberg theory shows that the strong dependence of the superconducting transition temperature on the species $M$ arises from these special phonons.