Session R30: Sr2RuO4 and other Triplet Superconductors

Exotic Oddness in Superconducting Sr2RuO4

The superconducting gap symmetry of Sr₂RuO₄ is still under debate. Most experiments suggest a triplet state, yet the best candidate order-parameter for odd-parity pairing fails to explain all experiments[1]. The most problematic issue is that the presence of nodes on the Fermi surface would rather support a d-wave symmetry[2]. A less discussed pairing function is odd-frequency Cooper pairing which may explain the intrinsic Kerr effect in this system[3]. In our study, we solve the frequency dependent Eliashberg equation[4] to investigate whether or not this pairing symmetry appears in the leading gap symmetries of Sr₂RuO₄. We used a DFT+DMFT calculation to calculate its spin excitation spectra and in turn the spin-fluctuation mediated pairing interaction. Focusing on the triplet pairing channel, we show that Sr₂RuO₄ has a stronger tendency towards odd-frequency superconductivity than towards any p-wave state.

[1] Mackenzie et al., npj Quantum Materials 2, 40 (2017)
[2] Hassinger et al., Phys. Rev. X 7, 011032 (2017)
[3] Komendová and Black-Schaffer, Phys. Rev. Lett. 119, 087001 (2017)
[4] Nourafkan et al., Phys. Rev. Lett. 117, 137001 (2016)   

Consequences of Deep Gap Minima in SrRuO for Thermal Transport

There exists an apparent conflict in experiments on unconventional superconductor Sr2RuO4 concerning the nature of the superconducting order parameter. In particular, despite evidence of chiral p-wave pairing from various experiments, thermal conductivity measurements show quasiparticle transport down to T_c/30 suggesting the existence of gap nodes. To quantify the import of this observation, we solve self-consistent BdG equations with dilute unitary scatterers to determine various low-energy properties including density of states, inverse participation ratio, and thermal conductivity. Although chiral p-wave cannot generically exhibit a true gap node, the gap structure obtained for a two-band quasi-1D model from weak-coupling RG has an anisotropic gap with deep minima. We compare our results with d-wave and anisotropic s-wave (which both have true nodes) and find a filling in of zero energy density of states for both d-wave and chiral p-wave in contrast to anisotropic s-wave. These results are augmented with a calculation of thermal conductivity using self-consistent T-matrix approximation, and together suggest anisotropic chiral p-wave cannot be ruled out by recent thermal conductivity measurements, though angle dependence may provide additional insight into the pairing symmetry.   

Superconducting pairing in Sr2RuO4 from weak to intermediate coupling

The unconventional superconductivity in Sr2RuO4 continues to attract considerable interest. While many measurements can be interpreted on the basis of chiral p-wave pairing, a number of notable exceptions hinder an unambiguous verification of such an order. The pairing mechanism also remains under debate. In this paper, with the effects of the sizable spin-orbit coupling accounted for, we reexamine the superconducting instabilities in Sr2RuO4 through systematic microscopic analysis within random phase approximation. Our calculations show that the odd-parity p-wave pairing is favored in the regime of extremely weak interactions, but that highly anisotropic even-parity pairings become most leading over a broad range of stronger interactions. These results could shed light on the nature of the enigmatic superconductivity in Sr2RuO4.   

FLEX analysis of the impact of strain and 3D coupling on the superconducting transition of Sr2RuO4

Analysis of the superconducting transition of Sr₂RuO₄ via application of the fluctuation exchange approximation (FLEX) to realistic tight-binding and interaction parameters leads to a d-wave pairing state with p-wave components induced through spin-orbit coupling. While the FLEX-generated superconducting state does not account for time-reversal symmetry breaking signatures observed in μSR and Kerr effect experiments, it is consistent with apparent line-nodes in thermodynamic data as well as the absence of significant observed Knight shifts across T_c on account of spin-orbit coupling rather than a fully-triplet pairing state. We present results for the transition temperature as a function of in-plane strain in the two-dimensional limit and show that, in accordance with experiment, T_c, is supressed rapidly when the Fermi level passes through the van Hove singularity in the γ band with no strain induced splitting of the transition. However, these results do not account for the initial enhancement of T_c as strain is increased from zero. We will also report the impact of 3D coupling on this analysis.   

17O NMR studies of Sr2RuO4 under uniaxial strain

Sr₂RuO₄ is a candidate for chiral odd-parity superconductivity with T_c~1.5 K, an interpretation supported by an unchanged ¹⁷O and ¹⁰¹Ru hyperfine shifts upon cooling through T_c. Recently, compressive strain was associated with a sharp peak in T_c, T_c^max~3.5 K, and connected to a Van-Hove Singularity (VHS). Normal state ¹⁷O NMR spectra, recorded at low temperature and in samples subject to compressive strain, exhibit corresponding singularities in hyperfine shifts. The results deviate significantly relative to expectations for the VHS, in that impacted susceptibilities are inferred to originate not just with d_xy orbitals, but also d_yz, d_xz. ¹⁷O NMR measurements in the superconducting state of strained samples are underway.   

Scanning SQUID Susceptometry of Sr2RuO4 Under Uniaxial Pressure

Anisotropic strain, as applied through uniaxial pressure, is expected to lift the degeneracy between the components of the proposed p_x±ip_y superconducting order parameter of Sr₂RuO₄. However, neither the resulting split transition nor the expected linear cusp in superconducting transition temperature, T_C, at low strain has been observed to date. Furthermore, measurements of the critical field anisotropy suggest that the order parameter may be of even parity at high values of anisotropic strain, where T_C is strongly enhanced. In this study, we will use scanning SQUID susceptometry to obtain measurements of T_C and changes in the penetration depth, λ, as a function of temperature and uniaxial pressure. We image strain inhomogeneity by mapping T_C with micron-scale spatial resolution and perform local measurements of the superfluid density in homogeneous regions. Penetration depth measurements yield insight into the symmetry of the order parameter and its dependence on strain.   

Edge Josephson Junction Detection of Topological Chiral Edge Current in Spin-triplet Superconductor Sr2RuO4 with a Calibrated Sensitivity

Sr₂RuO₄ is an unconventional superconductor predicted to have a spin-triplet, p-wave order parameter, however a full description of the order parameter has yet to be resolved experimentally despite two decades of research. Phase-sensitive measurements using AuIn-Sr₂RuO₄ SQUIDs on bulk crystals, first performed over a decade ago, clearly demonstrated that the order parameter has an odd parity, making the so called Γ₅, the chiral p-wave pairing state the most likely candidate. We have fabricated Josephson junctions between Al and the edges of thin (<1 μm) crystal plates of Sr₂RuO₄ to determine the precise pairing symmetry in the few-domain regime. We compare our results on flake corner junctions to those of bulk measurements, where neither a minimum nor maximum was observed at zero field in the I_c-H interference pattern. We also use junctions fabricated on single faces of the crystal to probe the existence of the predicted chiral edge currents. It is found that a non-zero remnant magnetic field exists within the Sr₂RuO₄ samples below T_c, even when subject to zero-field cooling. Together these results reaffirm that Sr₂RuO₄ has an odd-parity pairing symmetry, and provides strong support to the possibility of chiral p-wave, topological superconductivity in this material.   

Understanding the superconducting Sr2RuO4 through Sr2MoO4

Sr₂RuO₄ is widely conceived to be a candidate chiral p-wave superconductor. Various aspects of its unconventional pairing have been and are still being actively studied. By contrast, its nonsuperconducting iso-structural and iso-electronic analog, Sr₂MoO₄, has received far less attention. In the hope of obtaining deeper insight about the superconductivity in Sr₂RuO₄, we present a comparative study of Sr₂RuO₄ and Sr₂MoO₄, focusing on their electron correlations and superconducting instabilities. These are approached respectively by a slave-spin theory and random phase approximation. We will discuss the possible important characters of the two materials that may hold relevance for their distinct ground states.   

The magnon of SrRuO3 single crystal film by Neutron Inelastic Scattering

Low energy excitations such as magnon, plaron and phonon are primary properties tightly associated with unique physical phenomena of materials and can be probed by powerful inelastic neutron scattering usually in bulk crystal. In this study, we have used an inelastic neutron scattering on SrRuO3 thin films to investigate the magnon dispersion curve in this ferromagnetic system to better understand the underlying mechanisms. Inelastic scattering experiments were carried out in ANSTO SIKA and NIST SPINS. This is the first report to prove the existence of magnons in SrRuO2 system using an inelastic neutron scattering experiment on a thin film systems. We found that two magnon dispersion curves propagates along the [00l] direction and follows the quadratic (E ∝ Q2) relations which may be attributed to the tetragonal crystal structure of the films. One magnon has no gap and the other has a gap of 0.56meV at the zone center which correspond to J =1.55 and 1.76meV, respectively.   

Observation of two-dimensional high-Tc superconductivity in a Ca2RuO4 nanofilm single crystal

We report two-dimensional superconductivity from high-temperature in a Ca₂RuO₄ nano film single crystal. A thin film of Ca₂RuO₄ exhibits typical BKT transition behaviour around T_BKT = 30 K. We also found that the bias current applied to the thin film causes a SI transition at low temperatures. The film is superconductive for small bias currents and insulating for large bias currents. The two phases are well separated by the critical sheet resistance of the thin film 16.5 kΩ ≈ (8/π) h/4e². In addition to these findings, our results suggest the presence of superconducting fluctuations at a high temperature. The fabrication of nanofilms made of layered material enables us to discuss rich superconducting phenomena in ruthenates.   

Nonunitary triplet pairing in the noncentorsymmetric superconductor LaNiC2

In muon spin-relaxation experiments the noncentorsymmetric superconductor LaNiC₂ showed that on entering the superconducting state it also breaks time-reversal symmetry [1]. Based on group theoretical considerations it was already shown that the breaking of time-reversal symmetry is only compatible with nonunitary triplet pairing states [2,3]. To investigate the pairing mechanism by which this comes about and the possible role that the lack of inversion symmetry, we have generalized the relativistic spin-polarized version of Korringa-Kohn-Rostoker method for the solution of the Dirac-Bogoliubov-de Gennes equations [4]. Based on a particularly efficient parametrization of the pairing interaction afforded by the density-functional theory for superconductors different orbital-selective pairing models have been studied in quantitative detail.


[1] A. D. Hillier, J. Quintanilla, and R. Cywinski, Phys. Rev. Lett. 102, 117007 (2009)

[2] Jorge Quintanilla, Adrian D. Hillier, James F. Annett, and R. Cywinski, Phys. Rev. B 82, 174511 (2010)

[3] A. D. Hillier, J. Quintanilla, B. Mazidian, J. F. Annett, and R. Cywinski, Phys. Rev. Lett. 109, 097001 (2012)

[4] Gabor Csire, Balazs Ujfalussy, Jozsef Cserti, and Balazs Gyorffy, Phys. Rev. B 91, 165142 (2015)   

Evidence for triplet superconductivity near an antiferromagnetic instability in CrAs

Unconventional superconductivity, where the Cooper pairs are bound by a mechanism other than the conventional electron-phonon pairing mechanism described by BCS theory, has often been found to occur in close proximity to magnetic order in systems such as the cuprates, iron pnictides and heavy fermion superconductors. Recently CrAs has been discovered to show superconductivity as the helimagnetic order is suppressed by applying pressure[1], suggesting possible unconventional superconductivity. To reveal the nature of the superconducting order parameter of CrAs, we performed measurements of the angular dependence of upper critical field(B_c2) of CrAs under pressure using a triple-axis vector magnet. We find a clear anisotropy of B_c2 in the bc plane, where both two-fold and six-fold oscillatory components are observed, which are consistent with an unconventional odd-parity triplet superconducting state[2].

[1] W. Wu et al., Nat. Commun. 5, 5508 (2014).
[2] C. Y. Guo et al., arXiv: 1710. 06707 (2017).   

Odd-Frequency Pairing and the Kerr Effect in the Heavy-Fermion Superconductor UPt3

Recent observations of the Kerr effect in the low-temperature superconducting phase of UPt₃ indicate the presence of a time-reversal symmetry-breaking complex two-component order parameter. Subsequent theoretical work has shown that in order to obtain a sizable Kerr rotation angle in UPt₃ the system must have finite inter-sublattice scattering amplitudes and the order parameter must possess an inter-sublattice non-unitary component. In this work, we demonstrate that this exact same mechanism leading to the emergence of a Kerr effect in UPt₃ also guarantees the presence of odd-frequency superconducting pairing. We characterize the different odd-frequency pairing channels allowed in this system and discuss their relationship to the appearance of the finite Kerr rotation angle.