Fully gapped superconducting state in interstitial-carbon-doped Zr₅Pt₃

We report a comprehensive study of the Zr5Pt3Cx superconductors, with interstitial carbon between 0 and 0.3. At a macroscopic level, their superconductivity, with Tc ranging from 4.5 to 6.3 K, was investigated via electricalresistivity, magnetic-susceptibility, and specific-heat measurements. The upper critical fields ??0Hc2 - 7 T were determined mostly from measurements of the electrical resistivity in applied magnetic field. The microscopic electronic properties were investigated by means of muon-spin rotation and relaxation (??SR) and nuclear magnetic resonance (NMR) techniques. In the normal state, NMR relaxation data indicate an almost ideal metallic behavior, confirmed by band-structure calculations, which suggest a relatively high electronic density of states at the Fermi level, dominated by the Zr 4d orbitals. The low-temperature superfluid density, obtained via transverse-field ??SR, suggests a fully gapped superconducting state in Zr5Pt3 and Zr5Pt3C0.3, with zerotemperature gap ???0 = 1.20 and 0.60 meV and magnetic penetration depth ??0 = 333 and 493 nm, respectively. The exponential dependence of the NMR relaxation rates below Tc further supports nodeless superconductivity. The absence of spontaneous magnetic fields below the onset of superconductivity, as determined from zero-field ??SR measurements, confirms the preserved time-reversal symmetry in the superconducting state of Zr5Pt3Cx. In contrast to a previous study, our ??SR and NMR results suggest conventional superconductivity in the Zr5Pt3Cx family, independent of the C content.