Fully gapped superconducting state in interstitial-carbon-doped Zr5Pt3

Abstract

We report a comprehensive study of the ${\mathrm{Zr}}_{5}{\mathrm{Pt}}_{3}{\mathrm{C}}_{x}$ superconductors, with interstitial carbon between 0 and 0.3. At a macroscopic level, their superconductivity, with ${T}_{c}$ ranging from 4.5 to 6.3 K, was investigated via electrical-resistivity, magnetic-susceptibility, and specific-heat measurements. The upper critical fields ${\ensuremath{\mu}}_{0}{H}_{\mathrm{c}2}\ensuremath{\sim}7$ 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 ($\ensuremath{\mu}\mathrm{SR}$) 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 $\ensuremath{\mu}\mathrm{SR}$, suggests a fully gapped superconducting state in ${\mathrm{Zr}}_{5}{\mathrm{Pt}}_{3}$ and ${\mathrm{Zr}}_{5}{\mathrm{Pt}}_{3}{\mathrm{C}}_{0.3}$, with zero-temperature gap ${\mathrm{\ensuremath{\Delta}}}_{0}=1.20$ and 0.60 meV and magnetic penetration depth ${\ensuremath{\lambda}}_{0}$ = 333 and 493 nm, respectively. The exponential dependence of the NMR relaxation rates below ${T}_{c}$ further supports nodeless superconductivity. The absence of spontaneous magnetic fields below the onset of superconductivity, as determined from zero-field $\ensuremath{\mu}\mathrm{SR}$ measurements, confirms the preserved time-reversal symmetry in the superconducting state of ${\mathrm{Zr}}_{5}{\mathrm{Pt}}_{3}{\mathrm{C}}_{x}$. In contrast to a previous study, our $\ensuremath{\mu}\mathrm{SR}$ and NMR results suggest conventional superconductivity in the ${\mathrm{Zr}}_{5}{\mathrm{Pt}}_{3}{\mathrm{C}}_{x}$ family, independent of the C content.