  The superconducting properties of two beta-pyrochlore oxides, CsOs2O6 and
RbOs2O6, are studied by thermodynamic and transport measurements using
high-quality single crystals. It is shown that the character of
superconductivity changes systematically from weak coupling for CsOs2O6 to
moderately strong coupling for RbOs2O6, and finally to extremely strong
coupling with BCS-type superconductivity for KOs2O6, with increasing Tc.
Strong-coupling correction analyses of the superconducting properties reveal
that a low-energy rattling mode of the alkali metal ions is responsible for the
mechanism of the superconductivity in each compound. The large enhancement of
Tc from Cs to K is attributed to the increase in the electron-rattler coupling
with decreasing characteristic energy of the rattling and with increasing
anharmonicity. The existence of weak anisotropy in the superconducting gap or
in the electron-rattler interactions is found for the Cs and Rb compounds.
