Effect of Rattling Phonon on Superconductivity of KOs₂O₆

We model the electron coupling to anharmonic (rattling) mode in β-pyrochlore superconductor KOs₂O₆ by a sharply peaked electron-phonon coupling function centered at the mode energy. The strong-coupling Eliashberg equations are solved for the transition temperature and the gap function for a series of temperatures below T_c. From these solutions we obtain the temperature dependence of the gap edge, the nuclear magnetic resonance (NMR) relaxation rate and the microwave conductivity for several values of the electron-phonon coupling
parameter. The result are compared with the available experimental results.