Strong-Coupling Theory of Rattling-Induced Superconductivity

TL;DR

This paper investigates how anharmonic local oscillations, or rattling, in cage structures can enhance superconductivity by analyzing the anharmonic Holstein model with Migdal-Eliashberg theory, revealing conditions for increased $T_c$.

Contribution

It introduces a theoretical framework showing how anharmonicity influences strong electron-phonon coupling and superconducting transition temperature in rattling systems.

Findings

Strong coupling develops when the potential is wide and flat.

Superconducting $T_c$ increases with anharmonicity up to a point.

Very strong anharmonicity can decrease $T_c$ due to double-well potentials.

Abstract

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.