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We report muon spin rotation ($\mu$SR) studies of the superconducting properties as a function of chemical and hydrostatic pressure on the cubic ternary intermetallic (Ca$_{x}$Sr$_{1-x}$)$_{3}$Rh$_{4}$Sn$_{13}$ compounds, which feature strong coupling phonon-mediated BCS superconductivity and a structural phase transition a critical pressure p$_c$ associated with a charge density wave (CDW) formation$\,[1]$. A strong enhancement of the superfluid density and a pronounced maximum in the pairing strength provide evidence of a quantum critial point at p$_c$, which separates a superconducting phase coexisting with CDW from a pure superconducting phase. In both phases superconductivity has a phonon-mediated BCS $s$-wave character. Together with the related isoelectronic compound Ca$_{3}$Ir$_{4}$Sn$_{13}$ $[2]$, this system shows that conventional BCS superconductors in the presence of competing orders may display behavior and characteristics of unconventional superconductors.
$[1]$ S. K. Goh, et al., Phys. Rev. Lett. 114, 097002 (2015)
$[2]$ P. K. Biswas, et al., Phys. Rev. B 92, 195122 (2015)
