Strong enhancement of $s$-wave superconductivity near a quantum critical point of (Ca$_{1-x}$Sr$_{x}$)$_{3}$\-Ir$_{4}$\-Sn$_{13}$ and (Ca$_{1-x}$Sr$_{x}$)$_{3}$\-Rh$_{4}$\-Sn$_{13}$

We report microscopic studies by muon spin rotation as a function of pressure of the ~(Ca$_{1-x}$Sr$_{x}$)$_{3}$\-Ir$_{4}$\-Sn$_{13}$ and (Ca$_{1-x}$Sr$_{x}$)$_{3}$\-Rh$_{4}$\-Sn$_{13}$ cubic compounds, which display superconductivity and a structural phase transition associated with the formation of a charge density wave (CDW)[1]. In Ca$_{3}$\-Ir$_{4}$\-Sn$_{13}$ we find a strong enhancement of the superfluid density and a dramatic increase of the pairing strength above a pressure of $\approx 1.6 $ GPa giving direct evidence of the presence of a quantum critical point separating a superconducting phase coexisting with CDW from a pure superconducting phase [2]. The superconducting order parameter in both phases has the same $s$-wave symmetry. Similar behavior is found in the other family. In spite of the conventional phonon-mediated BCS character of these weakly correlated 3-4-13 systems, the dependence of the effective superfluid density on the critical temperature put these compounds in the ``Uemura'' plot close to unconventional superconductors. These systems exemplify that conventional BCS superconductors can also display 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 (2015).