Peak in the critical current density in (Ca$_{x}$Sr$_{1-x}$)$_3$Rh$_4$Sn$_{13}$ tuned towards the structural quantum critical point

(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.