Time-reversal symmetry breaking in the noncentrosymmetric Zr$_3$Ir superconductor

TL;DR

This paper reports the discovery of Zr3Ir as an unconventional noncentrosymmetric superconductor that breaks time-reversal symmetry, characterized by muon-spin rotation/relaxation techniques and supported by electronic structure calculations.

Contribution

It introduces Zr3Ir as a new noncentrosymmetric superconductor with broken time-reversal symmetry, combining experimental and theoretical analysis.

Findings

Zr3Ir has a superconducting transition temperature of 2.3 K.

Muon experiments reveal spontaneous magnetic fields below Tc.

Superfluid density indicates a fully-gapped superconducting state.

Abstract

We report the discovery of Zr$_3$Ir as a new type of unconventional noncentrosymmetric superconductor (with $T_c = 2.3$ K), here investigated mostly via muon-spin rotation/relaxation ($\mu$SR) techniques. Its superconductivity was characterized using magnetic susceptibility, electrical resistivity, and heat capacity measurements. The low-temperature superfluid density, determined via transverse-field $\mu$SR and electronic specific heat, suggests a fully-gapped superconducting state. The spontaneous magnetic fields, revealed by zero-field $\mu$SR below $T_c$, indicate the breaking of time-reversal symmetry in Zr$_3$Ir and, hence, the unconventional nature of its superconductivity. By using symmetry arguments and electronic-structure calculations we obtain a superconducting order parameter that is fully compatible with the experimental observations. Hence, our results clearly suggest that Zr$_3$Ir represents a new member of noncentrosymmetric superconductors with broken time-reversal symmetry.

Equations

$$A_{\mathrm{TF}}=A_{\mathrm{s}}{e}^{-{\sigma }^2{t}^2/2}\cos ({\gamma }_{\mu }{B}_{\mathrm{s}}t+\varphi )+A_{\mathrm{bg}}\cos ({\gamma }_{\mu }{B}_{\mathrm{bg}}t+\varphi ).$$

$${\sigma }_{\mathrm{sc}}(h)=0.172\frac{{\gamma }_{\mu }{\Phi }_0}{2\pi }(1-h)[1+1.21(1-\sqrt{h}{)}^3]{\lambda }_{\mathrm{eff}}^{-2},$$

$$A_{\mathrm{ZF}}=A_{\mathrm{s}}\left\{\frac{1}{3}+\frac{2}{3}(1-\Lambda t){\mathrm{e}}^{-\Lambda t}\right\}+A_{\mathrm{bg}}.$$

Full text

Unconventional superconductors, in addition to $U(1)$ gauge symmetry, also break other types of symmetry Sigrist and Ueda (1991); Tsuei and Kirtley (2000). Among them, the breaking of time-reversal symmetry (TRS) below $T_{c}$ has been widely studied, in particular by means of zero-field muon-spin relaxation (ZF-$\mu$SR). As a very sensitive technique, $\mu$SR is able to detect the tiny spontaneous magnetic fields appearing below the onset of superconductivity (SC). Unconventional superconductors known to exhibit TRS breaking include, e.g., Sr2RuO4 Luke et al. (1998), PrOs4Sb4 Aoki et al. (2003), UPt3 Luke et al. (1993), LaNiGa2 Hillier et al. (2012), LaNiC2, La${}_{7}T_{3}$, and Re$T$ ($T$ = transition metal) Hillier et al. (2009); Barker et al. (2015); Shang et al. (2018a, b); Singh et al. (2014, 2017, 2018a, 2018b). The latter three also represent typical examples of noncentrosymmetric superconductors (NCSCs). In this case, the lack of space-inversion symmetry leads to an electric field gradient and, hence, to an antisymmetric spin-orbit coupling (ASOC), which splits the Fermi surface with opposite spin configurations. Often the strength of ASOC exceeds the superconducting energy gap, and the pairing of electrons belonging to different spin-split bands results in a mixture of singlet and triplet states. Due to such mixed pairing, NCSCs can exhibit significantly different properties from their conventional counterparts, e.g. a nodal superconducting gap Yuan et al. (2006); Nishiyama et al. (2007); Bonalde et al. (2005); Pang et al. (2015); Adroja et al. (2015), upper critical fields exceeding the Pauli limit Bauer et al. (2004); Carnicom et al. (2018); Shang et al. (2018a) or, as recently proposed, topological superconductivity Ali et al. (2014); Sun et al. (2015); Kim et al. (2018). In turn, the structure and/or symmetry may be important in determining the effects of ASOC on the superconducting properties Anand et al. (2014).

In general, the breaking of time-reversal and spatial-inversion symmetries are not necessarily correlated. Indeed, many NCSCs, such as Mo3Al2C Bauer et al. (2010), Mo3Rh2N Shang et al. (2018c), La$T$Si3 Anand et al. (2011, 2014); Smidman et al. (2014), and Mg10Ir19B16 Aczel et al. (2010) do not exhibit spontaneous magnetic fields in the superconducting state and hence TRS is preserved. TRS breaking in NCSCs is supposed to arise mostly from unconventional pairing mechanisms. For example, LaNiC2 is proposed to be a pure nonunitary triplet SC Hillier et al. (2009); Quintanilla et al. (2010) with pairing between same spins in two different orbitals Weng et al. (2016).

Despite numerous examples of NCSCs, to date only a few of them are known to break TRS in their superconducting state. The causes of such selectivity remain largely unknown. Therefore, the availability of a new NCSC with broken TRS, such as Zr3Ir reported here, would improve our understanding of the interplay between the different types of symmetry. In this Letter, we report systematic studies of Zr3Ir by means of magnetization, transport, thermodynamic and muon-spin relaxation ($\mu$SR) measurements. The key observation of spontaneous magnetic fields, revealed by zero-field (ZF) $\mu$SR, indicates that Zr3Ir represents a new member of the NCSC family, making it a benchmark for the current theories of TRS breaking and unconventional SC in NCSCs.

Polycrystalline Zr3Ir samples were prepared by arc melting method Sup . The crystal structure and the sample purity were checked via x-ray powder diffraction using a Bruker D8 diffractometer. Consistent with previous results Cenzual and Parthié (1985), Zr3Ir crystallizes in a tetragonal $\alpha$-V3S-type noncentrosymmetric structure with space group $I\bar{4}2m$ (121) Sup . The magnetic susceptibility, electrical resistivity, and specific heat measurements were performed on a Quantum Design magnetic and physical property measurement system. The $\mu$SR measurements were carried out on the GPS and LTF spectrometers of the $\pi$M3 beam line at the Paul Scherrer Institut (PSI), Villigen, Switzerland.