Possible unconventional pairing in (Ca,Sr)3(Ir,Rh)4Sn13 superconductors revealed by controlling disorder

We study the evolution of temperature-dependent resistivity with added pointlike disorder induced by 2.5 MeV electron irradiation in stoichiometric compositions of the ``3-4-13'' stannides, ${(\text{Ca,Sr})}₃{(\text{Ir,Rh})}₄{\text{Sn}}₁₃$. Three of these cubic compounds exhibit a proposed microscopic coexistence of charge density wave (CDW) order and superconductivity (SC), while ${\text{Ca}}₃{\text{Rh}}₄{\text{Sn}}₁₃$ does not develop CDW order. As expected, the CDW transition temperature ${T}_{\text{CDW}}$ is universally suppressed by irradiation in all three compositions. The superconducting transition temperature, ${T}_c$, behaves in a more complex manner. In ${\text{Sr}}₃{\text{Rh}}₄{\text{Sn}}₁₃$, it increases initially in a way consistent with a direct competition of CDW and SC, but quickly saturates at higher irradiation doses. In the other three compounds, ${T}_c$ is monotonically suppressed by irradiation. The strongest suppression is found in ${\text{Ca}}₃{\text{Rh}}₄{\text{Sn}}₁₃$, which does not have CDW order. We further examine this composition by measuring the London penetration depth $\ensuremath{\lambda}(T)$, from which we derive the superfluid density. The result unambiguously points to a weak-coupling, full single gap, isotropic superconducting state. Therefore we must explain two seemingly incompatible experimental observations: a single isotropic superconducting gap and a significant suppression of ${T}_c$ by nonmagnetic disorder. We conduct a quantitative theoretical analysis based on a generalized Anderson theorem which points to an unconventional multiband ${s}^{+\ensuremath{-}}$-pairing state where the sign of the order parameter is different on one (or a small subset) of the smaller Fermi surface sheets but remains isotropic and overall fully gapped.