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We report microscopic studies by muon spin rotation/relaxation as a function of pressure of the Ca3Ir4Sn13 and Sr3Ir4Sn13 cubic compounds, which are members of the (Ca1−xSrx)3Ir4Sn13 system displaying superconductivity and a structural phase transition associated with the formation of a charge density wave (CDW). We find a strong enhancement of the superfluid density and a dramatic increase of the pairing strength above a pressure of ≈ 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. The superconducting order parameter in both phases has the same s-wave symmetry. In spite of the conventional phonon-mediated BCS character of the weakly correlated (Ca1−xSrx)3Ir4Sn13 system, the dependence of the effective superfluid density on the critical temperature puts this compound in the "Uemura" plot close to unconventional superconductors. This system exemplifies that conventional BCS superconductors in the presence of competing orders or multi-band structure can also display characteristics of unconventional superconductors. INTRODUCTIONThe interplay between different electronic ground states is one of the fundamental topics in condensed matter physics and is well apparent in phase diagrams as a function of doping, pressure or magnetic fields, resulting in various forms of coexistence, cooperation or competition of the order parameters [1][2][3][4]. Particularly interesting are the regions at phase boundaries or at quantum critical points (QCPs) where different quantum states meet [5]. Very often magnetism and superconductivity are involved and, in spite of diverse structural and physical properties, many compounds show characteristic phase diagrams where superconductivity is found in the vicinity of electronic instabilities of magnetic (mainly antiferromagnetic) origin. In this case spin fluctuations are predominantly considered at the heart of the mechanisms leading to pairing and superconductivity is unconventional. Less common is the case where the electronic instability is linked to the formation of a charge density wave (CDW), which is based on the same electron-phonon interaction found in conventional superconductors.Ternary intermetallic stannide compounds such as R 3 T 4 Sn 13 , where R =La, Ca, Sr and T =Ir, Rh [6,7] are of particular interest because they exhibit many physical properties such as superconductivity, magnetic or charge order, and structural instabilities. The quasiskutteridite cubic superconductor (Ca,Sr) 3 Ir 4 Sn 13 and the related (Ca,Sr) 3 Rh 4 Sn 13 have recently attracted attention because of the presence of a pressure induced structural phase transition at a temperature T * , the possible coexistence of superconducting and charge density wave states, and a putative quantum critical point [8][9][10][11][12][13][14][15][16]. The role and interplay of these degrees of freedom remain a central issue also in many unconventional superconductors, as demonstrated by the recent observa...