Electron–phonon superconductivity in C-doped topological nodal-line semimetal Zr₅Pt₃: a muon spin rotation and relaxation (μSR) study

Abstract

In the present work, we demonstrate that C-doped Zr5Pt3 is an electron–phonon superconductor (with critical temperature T C = 3.8 K) with a nonsymmorphic topological Dirac nodal-line semimetal state, which we report here for the first time. The superconducting properties of Zr5Pt3C0.5 have been investigated by means of magnetization, resistivity, specific heat, and muon spin rotation and relaxation (μSR) measurements. We find that at low temperatures, the depolarization rate is almost constant and it can be well described by a single-band s‐wave model with a superconducting gap of 2Δ(0)/k B T C = 3.84, somewhat higher than the value of BCS theory. From the transverse field μSR analysis, we estimate the London penetration depth λ L = 469 nm, superconducting carrier density n s = 1.83 × 1026 m−3, and effective mass m* = 1.428m e. The zero field μSR confirms the absence of any spontaneous magnetic field in the superconducting ground state. In order to gain additional insights into the electronic ground state of C-doped Zr5Pt3, we also performed first-principles calculations within the framework of density functional theory (DFT). The observed homogenous electronic character of the Fermi surface as well as the mutual decrease of T C and density of states at the Fermi level are consistent with the experimental findings of this study. However, the band structure reveals the presence of robust, gapless fourfold-degenerate nodal lines protected by 63 screw rotations and glide mirror planes. Therefore, Zr5Pt3 represents a novel, unprecedented condensed matter system to investigate the intricate interplay between superconductivity and topology.

Fully gapped superconducting state in interstitial-carbon-doped Zr5Pt3

“…However, recent muon-spin rotation and relaxation (μSR) results are consistent with a conventional s-wave pairing in Zr 5 Pt 3 C 0.5 [20]. More intriguingly, theoretical calculations predict that Zr 5 Pt 3 C x to be Dirac nodal-line semimetals and, as such, good candidates for realizing topological SC [20].…”

“…In carbon-intercalated Zr 5 Pt 3 C x , the T c value depends nonmonotonically on x, first increasing up to 7 K for x = 0.3, then decreasing to ∼4 K as the amount of intercalated C is further increased [16,20]. The first electronic specific-heat and magnetic penetration-depth studies suggested that Zr 5 Pt 3 and Zr 5 Pt 3 C 0.3 are nodal superconductors, implying their unconventional SC character [16].…”

“…The first electronic specific-heat and magnetic penetration-depth studies suggested that Zr 5 Pt 3 and Zr 5 Pt 3 C 0.3 are nodal superconductors, implying their unconventional SC character [16]. However, recent muon-spin rotation and relaxation (μSR) results are consistent with a conventional s-wave pairing in Zr 5 Pt 3 C 0.5 [20]. More intriguingly, theoretical calculations predict that Zr 5 Pt 3 C x to be Dirac nodal-line semimetals and, as such, good candidates for realizing topological SC [20].…”

Nodeless time-reversal symmetry breaking in the centrosymmetric superconductor Sc$_5$Co$_4$Si$_{10}$ probed by muon-spin spectroscopy

“…The presence of a flux-line lattice in the superconducting state results in an inhomogeneous field distribution within the sample, which in turn induces a faster decay in the asymmetry spectra below T C . The time evolution of the TF-µSR data at all temperatures above and below T C is best described by a sinusoidal oscillatory function damped with a Gaussian relaxation arising from muons implanted in the sample and an oscillatory background term from muons in the silver sample holder that do not depolarize [39][40][41][42]:…”

Nodeless time-reversal symmetry breaking in the centrosymmetric superconductor Sc5Co4Si10 probed by muon-spin spectroscopy

“…The presence of a flux-line lattice in the superconducting state results in an inhomogeneous field distribution within the sample, which in turn induces a faster decay in the asymmetry spectra below T C . The time evolution of the TF-μSR data at all temperatures above and below T C is best described by a sinusoidal oscillatory function damped with a Gaussian relaxation arising from muons implanted in the sample and an oscillatory background term from muons in the silver sample holder that do not depolarize [39][40][41][42]:…”