In order to clarify the mechanism of the enhancement of superconducting transition temperature $T_{ \rm c}$ due to anharmonic local oscillation of a guest ion in a cage composed of host atoms, i.e., { \it rattling}, we analyze the anharmonic Holstein model by applying the Migdal-Eliashberg theory. From the evaluation of the normal-state electron-phonon coupling constant, it is found that the strong coupling state is developed, when the bottom of a potential for the guest ion becomes wide and flat. Then, $T_{ \rm c}$ is enhanced with the increase of the anharmonicity in the potential, although $T_{ \rm c}$ is rather decreased when the potential becomes a double-well type due to very strong anharmonicity. From these results, we propose a scenario of anharmonicity-controlled strong-coupling tendency for superconductivity induced by rattling. We briefly discuss possible relevance of the present scenario with superconductivity in $\beta$-pyrochlore oxides.
Categories: cond-mat.supr-con cond-mat.mtrl-sci