Fully-gapped superconducting state in interstitial-carbon-doped Zr5Pt3

Abstract

We report a comprehensive study of the Zr${}_5$Pt${}_3$C${}_x$ superconductors, with interstitial carbon comprised 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 $\hat{I}{¼}_0{H}_{c2}$ $\sim$ 7 T were determined mostly from measurements of the electrical resistivity in applied magnetic fields. The microscopic electronic properties were investigated by means of muon-spin rotation and relaxation ($\hat{I}¼$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 4$d$ orbitals. The low-temperature superfluid density, obtained via transverse-field $\hat{I}¼$SR, suggests a fully-gapped superconducting state in Zr${}_5$Pt${}_3$ and Zr${}_5$Pt${}_3$C${}_{0.3}$, with a zero-temperature gap $\hat{I}{”}_0$ = 1.20 and 0.60 meV and a magnetic penetration depth $\hat{I}{»}_0$ = 333 and 493 nm, respectively. The exponential dependence of the NMR relaxation rates below $T_c$ further supports a nodeless superconductivity. The absence of spontaneous magnetic fields below the onset of superconductivity, as determined from zero-field $\hat{I}¼$SR measurements, confirms a preserved time-reversal symmetry in the superconducting state of Zr${}_5$Pt${}_3$C${}_x$. In contrast to a previous study, our $\hat{I}¼$SR and NMR results suggest a conventional superconductivity in the Zr${}_5$Pt${}_3$C${}_x$ family, independent of the C content.

9 pages, 11 figures, accepted by Phys. Rev. B