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The effects of structural quantum criticality on the strong-couplingsuperconductivity of (Sr$_{1-x}$Ca$_x$)$_3$Rh$_4$Sn$_{13}$ have beeninvestigated via electrical resistivity and specific heat measurements. Wedemonstrate that the lattice specific heat at low temperatures considerablyincreases toward the structural quantum critical point (SQCP), $x_{\rmc}\approx0.9$. The superconducting gap increases with $x$ in the exact samefashion as the low-temperature lattice specific heat, clearly indicating thatthe abundant low-energy phonons cause strong-coupling superconductivity.Despite the electron-phonon interaction, which is much more enhanced than theelectron correlation, the low-temperature electrical resistivity near the SQCPvaries as $\propto T^2$. This finding suggests that structural quantumfluctuation affects the power law arising from the electron-phonon scattering.

Superconductivity enhanced by abundant low-energy phonons in (Sr$_{1-x}$Ca$_x$)$_3$Rh$_4$Sn$_{13}$