Superconductivity in the Filled Cage Compounds ${\mathrm{Ba}}_6{\mathrm{Ge}}_{25}$ and ${\mathrm{Ba}}_4{\mathrm{Na}}_2{\mathrm{Ge}}_{25}$

The clathrate compound $\mathrm{Ba}{}_6{\mathrm{Ge}}_{25}$ and its relatives consist of a rigid germanium skeleton, into which barium or other metal atoms are coordinated. These guest atoms can “rattle” freely at high temperatures, but in $\mathrm{Ba}{}_6{\mathrm{Ge}}_{25}$ some of them lock randomly into split positions below $T_S\sim 200\mathrm{K}$. The resulting bad metal undergoes a BCS-like superconducting transition at $T_c\simeq 0.24\mathrm{K}$. $T_c$ increases more than 16-fold, as $T_S$ is suppressed by hydrostatic pressure $p$, but changes only slightly with $p$ from $T_c\simeq 0.84\mathrm{K}$ in the undistorted sister compound $\mathrm{Ba}{}_4{\mathrm{Na}}_2{\mathrm{Ge}}_{25}$. The large enhancement of $T_c$ in $\mathrm{Ba}{}_6{\mathrm{Ge}}_{25}$ may be attributed mainly to the pressure tuning of strong disorder caused by the random displacement of Ba atoms at $T_S$.