Point contact spectroscopy and temperature dependence of resistivity of metallic sodium tungsten bronzes -Role of optical phonons

In this paper we report the results of electrical resistivity (1.5K < T <300K) and point contact spectroscopy (PCS) measurements on single crystals of metallic sodium tungsten bronze with varying sodium content. We have shown that the electron-phonon coupling function as measured through PCS can explain quantitatively the large temperature dependence of resistivity $\rho$ seen in these materials over the entire temperature range. The electron-phonon coupling function shows predominatly large peaks for phonon frequency range of 30meV < $\omega$ 100meV which match well with the calculated optical phonon modes for WO$_6$ octahedra. The integrated electron-phonon coupling constant $\lambda$ from this data is $\approx$ 0.25-0.45.