The effect of strong electron-rattling phonon coupling on some superconducting properties

Using the Eliashberg theory of superconductivity we have examined several properties of a model in which electrons are coupled only to rattling phonon modes represented by a sharp peak in the electron-phonon coupling function. Our choice of parameters was guided by experiments on β-pyrochlore oxide superconductor KOs₂Os₆. We have calculated the temperature dependence of the superconducting gap edge; the quasi-particle decay rate; the NMR relaxation rate assuming that the coupling between the nuclear spins and the conduction electrons is via a contact hyperfine interaction, which would be appropriate for the O-site in KOs₂Os₆; and the microwave conductivity. We examined the limit of very strong coupling by considering three values of the electron-phonon coupling parameter λ = 2.38, 3, and 5 and did not assume that the rattler frequency Ω₀ is temperature dependent in the superconducting state. We obtained a very unusual temperature dependence of the superconducting gap edge Δ(T), very much like the one extracted from photoemission experiments on KOs₂O₆. (author)