  (Ca$_{x}$Sr$_{1-x}$)$_3$Rh$_4$Sn$_{13}$ is a rare system that has been shown
to display an interesting interplay between structural quantum criticality and
superconductivity. A putative structural quantum critical point, which is
hidden beneath a broad superconducting dome, is believed to give rise to
optimized superconducting properties in
(Ca$_{x}$Sr$_{1-x}$)$_3$Rh$_4$Sn$_{13}$. However, the presence of the
superconducting dome itself hinders the examination of the quantum critical
point through electrical transport, as the transport coefficients vanish in the
superconducting state. Here, we use critical current density to explore within
the superconducting dome. Our measurements reveal a large enhancement of the
critical current density at the zero-temperature limit when the system is tuned
towards the structural quantum critical point.
