Split superconducting and time-reversal symmetry-breaking transitions in Sr2RuO4 under stress

Abstract

or most of its history, the superconductivity of strontium ruthenate (Sr 2 RuO 4) (ref. 1) has been understood in terms of an odd-parity two-component order parameter with equal-spin pairing in the RuO 2 planes: p x ± ip y (refs. 2-5). This order parameter is chiral: the Cooper pairs have angular momentum l = ±1. The evidence for chirality comes from the zero-field muon spin relaxation (ZF-μSR) data 6 , observation of a non-zero Kerr rotation below the critical temperature T c (ref. 7) and signs in the junction experiments of domains in the superconducting state 8,9 , while evidence for equal-spin pairing came from the absence of a change in the Knight shift below T c in nuclear magnetic resonance 10 and polarized neutron scattering 11 measurements. The Knight shift is related to the spin susceptibility; in conventional opposite-spin-pairing superconductors, it is suppressed below T c. However, in new measurements, it has been found that the Knight shift is, in fact, suppressed below T c (refs. 12-14), by a magnitude that is unlikely to be reconcilable with equal-spin pairing. This revision has called into question a number of other results on Sr 2 RuO 4. It raises a particular challenge for experiments that indicate chirality, because opposite-spin pairing implies an even-parity momentum-space gap structure. If the order parameter is constrained to be even parity, chiral, and composed of components that are degenerate on the tetragonal lattice of Sr 2 RuO 4 , the only possibility is d xz ± id yz order 15. Under conventional understanding, this is a highly unlikely order parameter because it

High-sensitivity heat-capacity measurements on Sr 2 RuO 4 under uniaxial pressure

“…In contrast to the ultrasound experiments, µSR does observe a split between the onset of spontaneous magnetism at T TRSB and that of superconductivity at Tc in samples subject to [100] uniaxial pressure (23). One possibility for the apparent discrepancy between the two experiments is the inability of ultrasound measurements performed at megahertz to resolve an attenuation discontinuity against the very large background attenuation seen in the [100] channel.…”

“…The second check that we have performed is explicitly informed by the findings reported in ref. 23, in which muon-spin relaxation data indicate that the onset of time-reversal symmetry breaking at T TRSB occurs in the range 1.2 to 1.5 K for all strains lower than that at which Tc is maximized. By multiple averaging of data from the temperature range of interest, we reduced the rms voltage noise on the thermocouple signal to 0.5 pV, giving a detection limit for a sharp secondary transition of only 0.3% of the size of the primary one or, more realistically, a detection limit of 5% for a secondary transition of width similar to the that of the primary one (see SI Appendix, Experimental Limits for full details).…”

“…In ref. 23 it was argued that the discrepancy between heatcapacity ratios and Tc slopes could be explained by higher-order terms that dominate the leading-order terms in the Ginzburg-Landau expansion even at relatively low strains. Here, we argue that although this is a reasonable hypothesis in the vicinity of the Lifshitz transition, where the evolution of the electronic structure is clearly nonlinear in strain, it appears less likely at low strains, and therefore that the absence of a resolvable second heat-capacity anomaly makes TRSB E -pairing dxz ± idyz order unlikely.…”

“…To investigate any order parameter with two degenerate components, whether or not it breaks time-reversal symmetry, uniaxial pressure is a powerful probe because it can split the degeneracy, creating a split superconducting phase transition (22). In a significant experimental advance, the muon-spin relaxation experiments have recently been extended to high uniaxial pressures (23). In line with naive expectation, the temperature at which time-reversal symmetry is broken (T TRSB ) splits from the main superconducting transition (Tc), with T TRSB remaining nearly pressure-independent while Tc increases under the application of the pressure.…”

Time-reversal symmetry breaking and multigap superconductivity in the noncentrosymmetric superconductor La7Ni3

“…We have discussed possible microscopic scenarios for the order parameter and pairing interactions of the superconducting phase. In order to pinpoint which of those possibilities is realized, further experimental work on single crystals of La 7 Ni 3 , in particular, uniaxial and hydrostatic pressure studies [78], theoretical modeling, and band structure calculations are required. fields starting from 5 mT to 90 mT by considering the onset of the diamagnetic signal.…”