Superconducting Transition in the $\beta$-Pyrochlore AOs$_2$O$_6$ (A=Cs, Rb, K) under Pressure

Pressure dependence of superconducting transition temperature $T_{\rm c}$ has been determined through the DC magnetic measurements under pressure up to $P$=10 GPa for $\beta$-pyrochlore oxides AOs$_2$O$_6$ with A=Cs ($T_{\rm c}$=3.3 K), Rb (6.3 K) and K (9.6 K). Both for A=Rb and Cs, $T_{\rm c}$ increases with increasing $P$ and shows a saturation at $T_{\rm cm}$$\sim$8.8 K, which is considered as the upper limit of $T_{\rm c}$ inherent in AOs$_2$O$_6$. In contrast, the $T_{\rm c}-P$ curve for KOs$_2$O$_6$ shows a sharp maximum of $\sim$10 K at $P$$\sim$0.5 GPa, and $T_{\rm c}$ is higher than $T_{\rm cm}$ for 0$\leq$$P$$\leq$1.5GPa, suggesting the enhanced superconductivity due to the rattling of K ions.