Pith. sign in

REVIEW 3 major objections 4 minor 66 references

Puzzling superconductivity in strontium ruthenate: then and now

T0 review · 3 major / 4 minor · reviewed 2026-08-01 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read The measured Kerr effect in Sr2RuO4 is reproduced by a chiral spin-singlet d-wave pairing state just as well as by the old chiral p-wave state, so Kerr data alone cannot fix the pairing symmetry.

desk verdict A useful but incomplete model calculation: the d-wave Hall spectrum is computed and the sum rules are nice, but the claimed compatibility with the Kerr experiment at 0.8 eV is not actually established. read the letter →

arxiv 2607.21194 v1 pith:L5ZPGKBE submitted 2026-07-23 cond-mat.supr-con

James F. Annett , Karol I. Wysokiński This is my paper · ORCID
classification cond-mat.supr-con
keywords Sr2RuO4chirald-wavepairingKerreffectHallconductanceBerrycurvaturesumrulef-sumspin-singletsuperconductivityunconventional
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper argues that the long-standing identification of strontium ruthenate as a chiral spin-triplet p-wave superconductor has been overturned by corrected Knight-shift experiments, which now favour spin-singlet pairing. To test whether the observed Kerr rotation is compatible with singlet pairing, the authors compute the Hall conductance for a chiral d-wave Eg state in a realistic three-orbital model. They find a non-zero Hall conductance whose spectrum is qualitatively similar to the earlier p-wave calculation, meaning the Kerr effect does not distinguish the two chiralities. The paper also derives two sum rules: one ties the low-frequency Hall conductance to Berry curvature of the Bogoliubov quasiparticle bands, the other ties the high-frequency optical Kerr response to the inter-orbital pairing amplitude. These sum rules show what a Kerr measurement actually probes and provide a route to discriminating between competing singlet states.

What carries the argument

A three-orbital tight-binding model of Sr2RuO4 with a chiral Eg gap function Δmm'(k) = sin(kz c/2)[Δx sin(kxa/2)cos(kya/2) + Δy cos(kxa/2)sin(kya/2)], solved self-consistently in the Bogoliubov–de Gennes equations. The Hall conductance is computed from interband optical transitions (Eq. 6), giving the Kerr angle. Two sum rules organize the response: the Berry curvature sum rule (Eq. 10) sets Re σxy(0) via the Chern-like integral over Bogoliubov bands, and the f-sum rule (Eq. 17) sets the high-frequency Kerr tail via the current commutator ⟨[jx,jy]⟩, which vanishes when the inter-orbital pairing Δab is turned off.

What would settle it

Compute the Hall conductance for the same Eg model with spin-orbit coupling included in the 6×6 Bogoliubov–de Gennes Hamiltonian. If Re σxy(0) or the f-sum-rule integral becomes zero, or the spectrum no longer resembles the p-wave case, the claim that the Kerr effect is compatible with spin-singlet Eg pairing is refuted. Alternatively, a high-precision measurement of the Kerr angle as a function of photon frequency that fails to show the 1/ω² tail predicted by the f-sum rule would count against the model.

Watch

Extended reading notes

Core claim

Using the same three-dimensional tight-binding parameters as earlier work, but omitting spin-orbit coupling, the authors solve the self-consistent Bogoliubov–de Gennes equations for a chiral dxz+idyz (Eg) spin-singlet pairing state of Sr2RuO4. The calculated Hall conductance σxy(ω) is non-zero and, over the relevant frequency range, qualitatively similar in both real and imaginary parts to the spectrum obtained for the chiral p-wave Eu state. The zero-frequency limit obeys a Berry-curvature sum rule, vanishing as T→Tc, while the high-frequency tail obeys an f-sum rule proportional to ⟨[jx,jy]⟩, which is nonzero only when inter-orbital pairing amplitude Δab is present. The authors conclude th

Load-bearing premise

The calculation leaves out spin-orbit coupling, which is known to be significant in Sr2RuO4; if spin-orbit coupling changes the Bogoliubov band curvatures or current matrix elements enough, the nonzero Hall conductance found for the Eg state could vanish or change sign.

Editorial extensions

If this is right

  • A non-zero Kerr effect is not evidence for chiral p-wave pairing; the chiral d-wave Eg singlet state reproduces the observed signal.
  • Observation of a Kerr rotation at optical frequencies in this model requires inter-orbital pairing, so a measured Kerr angle can be read as a probe of Δab.
  • The Berry curvature sum rule connects the d.c. Hall response to the full frequency spectrum, enabling numerical checks and predictions for terahertz experiments.
  • Among spin-singlet candidates, the Eg state has a symmetry-enforced two-fold degeneracy at Tc, so time-reversal breaking must occur exactly at Tc, unlike d+is or d+ig states that require separate transitions.
  • The two sum rules partition the Hall response into a low-frequency Berry-curvature part and a high-frequency inter-orbital part, meaning low-frequency and optical Kerr measurements probe different aspects of the pairing state.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Because the calculation deliberately omits spin-orbit coupling, a natural next test is to include SOC; if SOC substantially changes the Berry curvatures, the claimed compatibility could fail.
  • The sum-rule decomposition offers a way to discriminate singlet candidates: computing the same quantities for d+id, d+is, or d+ig states should give distinct Berry-curvature and commutator signatures, which could be compared to future optical measurements.
  • The experimental observation that the Tc–TTRSB splitting under uniaxial strain is quadratic, whereas the Eg state would give a linear splitting, suggests that strain experiments can distinguish the Eg state from d+ig; the present Kerr calculations do not resolve that question.
  • A testable prediction is that the Kerr angle at optical frequencies should scale with the inter-orbital pairing amplitude in the Eg scenario, so systematic doping or pressure studies that alter Δab should change the Kerr magnitude in a specific way.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The paper reviews the long-standing puzzle of the pairing symmetry in Sr2RuO4, focusing on the recent Knight-shift experiments that disfavor spin-triplet chiral p-wave pairing and on the Kerr-effect measurements that indicate time-reversal symmetry breaking. The authors then present new self-consistent Bogoliubov–de Gennes calculations for a chiral spin-singlet d-wave Eg (dxz+idyz) pairing state. They compute the Hall conductivity σxy(ω), verify two sum rules (a Berry-curvature sum rule and a current-commutator f-sum rule), and claim that the Hall conductance for the Eg state is nonzero and qualitatively similar to that previously found for the chiral p-wave Eu state. On this basis they argue that the observed Kerr effect is compatible with a spin-singlet Eg pairing state.

Significance. If substantiated, the result would be important: it would show that the Kerr effect alone does not discriminate between the spin-triplet chiral p-wave scenario and a spin-singlet chiral d-wave scenario, and it would identify inter-orbital pairing as a key ingredient for an optical-frequency Kerr signal. The two sum-rule identities are clean and their numerical verification (Fig. 3) is a genuine strength of the paper. However, the central claim that the calculated response is compatible with the measured 0.8 eV Kerr angle is not quantitatively supported, and the neglect of spin-orbit coupling leaves a material-specific gap in the argument. The significance therefore hinges on whether the authors can close that gap.

major comments (3)
  1. [Section IV, Eq. (20) and Fig. 3] The abstract and concluding section claim that the calculated d-wave Eg Hall conductance is 'qualitatively similar' to the p-wave result and hence compatible with the measured Kerr effect. But the experiments are at 0.8 eV, while the spectra in Fig. 2 are only shown up to about 0.1 eV. The paper itself notes in Eq. (20) that the high-frequency real part is controlled by the f-sum rule ∫ω′Imσxy(ω′)dω′, and the lower panel of Fig. 3 shows this sum to be much smaller than the Berry-curvature sum, because Δab is small. Since the authors never evaluate Re[σxy(0.8 eV)] or estimate a Kerr angle for the Eg state, the compatibility claim is not quantitatively supported. This is the load-bearing step connecting the calculation to the experiment, and it needs to be addressed directly.
  2. [Section IV, paragraph after Eq. (11)] The calculation omits spin-orbit coupling ('Using the same three-dimensional tight-binding parameters as Gradhand et al. and Gupta et al., but omitting spin-orbit coupling') in a material where SOC is known to be substantial. The Hall conductivity in this formalism depends on Berry curvatures and inter-band current matrix elements whose orbital and spin character can be strongly modified by SOC. Since the claim is about Sr2RuO4 specifically, the omission needs justification or a sensitivity test; otherwise the nonzero result may be an artifact of the simplified model.
  3. [Section IV, Fig. 1 and the sentence following it] The interaction parameters Uaa, Uab, Ucc are hand-picked and, as the authors state, Uaa was increased relative to Ref. [44] specifically to enlarge the α- and β-band gaps because those bands dominate σxy. This means the nonzero Hall response is partly built into the model by construction. The parameter choice is acknowledged as non-unique, but no sensitivity analysis is given, so the reader cannot assess how robust the 'qualitatively similar' conclusion is to reasonable parameter variations.
minor comments (4)
  1. [Title and header] The title contains 'then a nd now' and 'a nd' in the abstract; these should be 'then and now' and 'and'.
  2. [Section V, first paragraph] The text says the Hall conductance spectrum is 'shown in Fig. 1', but Fig. 1 shows the temperature-dependent gap parameters; the Hall spectrum is Fig. 2.
  3. [Section IV, Eq. (13)] The notation for the emergent gap relations is confusing: ∆y_bb′ = i∆x_aa′ appears to omit the appropriate orbital indices. Please clarify.
  4. [References] Several references have incomplete or malformed DOIs (e.g., Refs. [25], [62]) and the author affiliation string 'M. Curie-Sk/suppress lodowska' is corrupted.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity; Hall conductance is a forward calculation from an assumed chiral Eg gap, sum rules are independently proved/verified, and self-citations are not load-bearing.

full rationale

The paper's central claim is that the chiral d-wave Eg state gives a nonzero Hall conductance qualitatively similar to the chiral p-wave Eu state. This is obtained by a forward solution of the Bogoliubov-de Gennes equations with an assumed gap of the form sin(kz c/2)[...] (Eq. 11), using the same tight-binding parameters as Gradhand et al. and Gupta et al. The nonzero σxy(ω) follows from the assumed time-reversal-symmetry-breaking chiral state and the multi-orbital band structure; it is not fitted to the Kerr data. The two sum rules are either proved in the text (f-sum rule, Eqs. 17-19) or numerically verified against the computed spectrum (Berry-curvature sum rule, upper panel of Fig. 3), so citations to the authors' prior work [56] are not load-bearing. The adjustment of Uaa to increase the α/β gaps is a model-parameter choice motivated by which bands dominate the effect; it is not a fit to the predicted quantity, and the nonzero Hall effect does not depend on that tuning. The acknowledged lack of a quantitative calculation at 0.8 eV is an evidence/correctness limitation, not a circular step. Self-citations appear but do not reduce the argument to themselves.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

The calculation rests on a mean-field tight-binding model with hand-chosen interaction parameters and several unverified modeling assumptions: no SOC, and extension of a low-energy model to 0.8 eV. No new physical entities are introduced; the Eg pairing state is a previously proposed candidate.

free parameters (2)
  • U_aa, U_ab, U_cc = 1.60t, 0.60t, 0.3107t, where t=0.08162 eV
    Chosen by hand to yield Tc=1.5K and to enlarge α/β gaps because the Hall effect is dominated by these bands; the authors state the choice is not unique.
  • Tight-binding parameters = taken from Gradhand et al. (2013) / Gupta et al. (2022)
    Empirical band-structure parameters (hoppings, on-site energies, etc.) from earlier papers are inherited without re-derivation; the central calculation depends on them.
assumptions (5)
  • domain assumption Bogoliubov-de Gennes mean-field theory is valid for Sr2RuO4.
    The paper solves self-consistent BdG equations; mean-field treatment of unconventional superconductivity is standard but not derived in the paper.
  • domain assumption The Eg pairing state is the only d-wave state with symmetry-enforced degeneracy at Tc in D4h.
    Used to justify selecting dxz+idyz; this is a group-theoretic fact about the D4h point group, not re-derived here.
  • ad hoc to paper Spin-orbit coupling can be omitted without qualitatively changing the Hall response.
    The calculation explicitly omits SOC, yet real Sr2RuO4 has significant SOC; this is an unverified modeling assumption.
  • ad hoc to paper The low-energy three-orbital tight-binding model remains adequate for optical frequencies up to 0.8 eV via the 1/ω² asymptotic form.
    The calculated spectrum is limited to about 0.1 eV but is used to infer the Kerr signal at 0.8 eV.
  • standard math The current operator and completeness relation in the BdG basis are standard.
    Equations (8), (9), and (18) are used without proof; they are standard quantum-mechanical results.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Puzzling superconductivity in strontium ruthenate: then and now." pith.science (2026). https://pith.science/paper/L5ZPGKBE

@misc{pith2026260721194,
  author       = {Pith},
  title        = {Pith review of: Puzzling superconductivity in strontium ruthenate: then and now},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/L5ZPGKBE}},
  note         = {Machine review of arXiv:2607.21194}
}
abstract

Strontium ruthenate is a very interesting low temperature superconductor with relatively simple normal state and very puzzling superconducting state properties. Despite over thirty years of intensive research, even the precise symmetry of the order parameter is not known. In this paper we briefly review some of the key developments, focussing on some of the newer experiments, especially those which challenged the previous understanding that it is a spin triplet odd parity chiral p-wave superconductor. Since Sr$_2$RuO$_4$ now appears most probably a spin singlet superconductor we have calculated the Kerr effect for one candidate $d$-wave pairing state. We find that for the chiral $d$-wave $E_g$ pairing state the calculated Hall conductance is non-zero and qualitatively similar to that found earlier under the assumption of a chiral p-wave $E_u$ order parameter. We characterize the Hall conductance in relation to two sum rules, one related to Berry curvatures in the Bogoliubov quasiparticle states, and the other $f$-sum rule indicating the presence of inter-orbital pairing.

Figures

Figures reproduced from arXiv: 2607.21194 by the authors.

Figure 1
Figure 1. FIG. 1. Temperature-dependent gap parameters in the model [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Calculated Hall conductance [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Top panel: Berry curvature sum rule compared [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

66 extracted references · 37 canonical work pages

  1. [44]

    J. A. Duffy, S. M. Hayden, Y. Maeno, Z. Mao, J. Kulda4 and G. J. McIntyre Phys. Rev. Lett.85, 5412 (2000) DOI: https://doi.org/10.1103/PhysRevLett.85.5412

    doi:10.1103/physrevlett.85.5412 2000

  2. [1]

    K. A. M¨ uller, J. G. Bednorz, Z. Phys.B 64, 189 (1986). DOI: https://doi.org/10.1007/BF01303701

    doi:10.1007/bf01303701 1986

  3. [2]

    We conclude that the previous results of the invariance of the Knight shift in the SC state were due to instantaneous destruction of superconductivity by the RF pulses

    and (1) they found that its value is also unchanged from the normal state one below Tc. The technique used was nuclear- quadrupole-resonance under magnetic fields parallel to the RuO2 plane (ab direction). The magnetic field was 550 Oe or greater, and the lowest temperature was 97mK. This finding was consistent with other possible triplet states predicted fo...

    2020

  4. [3]

    accidental

    Note that for the specific pairing state considered here, the numerical magnitude of this sum is much smaller than found for the Berry curvature sum rule. That is because this sum rule is in effect a measure of the presence of the inter-orbital pairing ∆ ab in our gap model. The small value of the sum rule inte- gral shown in Fig. 3 is a consequence of the ...

    2022

  5. [4]

    A. P. Mackenzie, Y. Maeno, Rev. Mod. Phys. 75, 657 (2003). DOI: https://doi.org/10.1103/RevModPhys.75.657

    doi:10.1103/revmodphys.75.657 2003

  6. [5]

    T. M. Rice and M. Sigrist, J. Phys.: Condens. Matter 7, L643 (1995). DOI: 10.1088/0953-8984/7/47/002

    work page doi:10.1088/0953-8984/7/47/002 1995

  7. [6]

    First, we note that inside the integrand of Eq. 6 the product of Fermi functions [1 − f(En′ (k))]f(En(k)) can be re- placed by just f(En(k)), because the product term, f(En′ (k))f(En(k)), is symmetric in the states n and n′ and therefore sums to zero [ 56]. Carrying out the fre- quency integral in Eq. 17 we are left with terms like ∑ n′ Mxy = ∑ n′ ⟨nk | ˆ...

  8. [7]

    Maeno, H

    Y. Maeno, H. Hashimoto, K. Yoshida, S. Nishizaki, T. Fujita, J. G. Bednorz, F. Lichtenberg, Nature 372, 532 (1994). DOI: https://doi.org/10.1038/372532a0

    work page doi:10.1038/372532a0 1994

Show all 66 references
  1. [8]

    R. J. Cava, B. Batlogg, K. Kiyono, H. Takagi, J. J. Krajewski, W. F. Peck, Jr., L. W. Rupp, Jr., C. H. Chen, Phys. Rev. B 49, 11890 (1994). DOI: https://doi.org/10.1103/PhysRevB.49.11890

    1994 doi

  2. [9]

    Pustogow, Yongkang Luo, A

    A. Pustogow, Yongkang Luo, A. Chronister, Y.-S. Su, D. A. Sokolov, F. Jerzembeck, A. P. Macken- zie, C. W. Hicks, N. Kikugawa, S. Raghu, E. D. Bauer, S. E. Brown, Nature, 574, 72 (2019). DOI: https://doi.org/10.1038/s41586-019-1596-2

    2019 doi

  3. [11]

    [52] and Gupta et al

    Using the same three-dimensional tight-binding parameters as Gradhand et al. [52] and Gupta et al. [44], but omitting spin-orbit coupling, we solve the self-consistent Bogoliubov de Gennes equa- tions. Fig. 1 shows the results for the specific choice Uaa = Ubb = 1 .60t, Uab = 0...

  4. [12]

    Ishida, H

    K. Ishida, H. Mukuda, Y. Kitaoka, K. Asayama, Z. Q. Mao, Y. Mori, Y. Maeno, Nature 396, 658 (1998). DOI: https://doi.org/10.1038/25315

    1998 doi

  5. [13]

    Bey- ersdorf, M

    Jing Xia, Yoshiteru Maeno, Peter T. Bey- ersdorf, M. M. Fejer, Aharon Kapitulnik, Phys. Rev. Lett. 97, 167002 (2006). DOI: https://doi.org/10.1103/PhysRevLett.97.167002

    2006 doi

  6. [14]

    Sokolov, Fabian Jerzembeck, Clifford W

    Aaron Chronister, Andrej Pustogow Naoki Kikugawa, Dmitry A. Sokolov, Fabian Jerzembeck, Clifford W. Hicks, Andrew P. Mackenzie, Eric D. Bauer, Stu- art E. Brown, PNAS 118, e2025313118 (2021). DOI: https://doi.org/10.1073/pnas.2025313118

    2021 doi

  7. [15]

    Kenji Ishida, Masahiro Manago, Katsuki Kinjo, Yoshiteru Maeno, J. Phys. Soc. Jpn. 89, 034712 (2020). DOI: https://doi.org/10.7566/JPSJ.89.034712

    2020 doi

  8. [16]

    Petsch, et al., Phys. Rev. Lett. 125, 217004 (2020). DOI: https://doi.org/10.1103/PhysRevLett.125.217004

    2020 doi

  9. [17]

    Spa/suppress lek, M

    J. Spa/suppress lek, M. Fidrysiak, M. Zegrodnik, A. Bi- borski, Physics Reports 959, 1 (2022). DOI: https://doi.org/10.1016/j.physrep.2022.02.003

    2022 doi

  10. [18]

    Gingras, N

    O. Gingras, N. Allaglo, R. Nourafkan, M. Cˆ ot´ e, A.-M. S. Tremblay, Phys. Rev. B 106, 064513 (2022). DOI: 10.1103/PhysRevB.106.064513

    2022 doi

  11. [19]

    Matter 7, 10 (2022)

    Annette Bussmann-Holder, Hugo Keller, Condens. Matter 7, 10 (2022). DOI: https://doi.org/10.3390/condmat7010010

    2022 doi

  12. [20]

    P. W. Anderson, Science 235 1196-1198 (1987) DOI: 10.1126/science.235.4793.119

    1987 doi

  13. [21]

    T. A. Maier, M. Jarrell, T. C. Schulthess, P. R. C. Kent, and J. B. White, Phys. Rev. Lett. 95, 237001 (2005). DOI: https://doi.org/10.1103/PhysRevLett.95.237001

    2005 doi

  14. [22]

    Xiaoyu Deng, Kristjan Haule, and Gabriel Kotliar, Phys. Rev. Lett. 116, 256401 (2016) DOI: https://doi.org/10.1103/PhysRevLett.116.256401

    2016 doi

  15. [23]

    Stefan K¨ aser, Hugo U. R. Strand, Nils Wentzell, An- toine Georges, Olivier Parcollet and Philipp Hans- mann Phys. Rev. B 105, 155101 (2022). DOI: https://doi.org/10.1103/PhysRevB.105.155101

    2022 doi

  16. [24]

    Rømer, T

    Astrid T. Rømer, T. A. Maier, Andreas Kreisel, P. J. Hirschfeld and Brian M. Ander- sen, Phys. Rev. Research 4, 033011 (2022) DOI: https://doi.org/10.1103/PhysRevResearch.4.033011

    2022 doi

  17. [25]

    Maurice Rice, Manfred Sigrist, Physics Today 54, 42 (2001)

    Yoshiteru Maeno, T. Maurice Rice, Manfred Sigrist, Physics Today 54, 42 (2001). DOI: https://doi.org/10.1063/1.1349611

    2001 doi

  18. [26]

    Yoshiteru Maeno, Shingo Yonezawa, Aline Ramires, J. Phys. Soc. Jpn. 93, 062001 (2024). DOI: https://doi.org/10.7566/JPSJ.93.062001

    2024 doi

  19. [27]

    Bergemann, A

    C. Bergemann, A. P. Mackenzie, S. R. Julian, D. Forsythe, E. Ohmichi, Ad- vances in Physics, 52, 639 (2003). DOI: https://doi.org/10.1080/00018730310001621737

    2003 doi

  20. [28]

    Catherine Kallin, Rep. Prog. Phys. 75, 042501 (2012). DOI: 10.1088/0034-4885/75/4/042501

    2012 doi

  21. [29]

    Yoshiteru Maeno, Shunichiro Kittaka, Takuji Nomura, Shingo Yonezawa1, Kenji Ishida, J. Phys. Soc. Jpn. 81, 9 011009 (2012). DOI: https://doi.org/

    2012

  22. [30]

    Catherine Kallin, John Berlinsky, Rep. Prog. Phys. 79, 054502 (2016). DOI: 10.1088/003,4885/79/5/054502,

    2016 doi

  23. [31]

    Mackenzie, Thomas Scaffidi, Clifford W

    Andrew P. Mackenzie, Thomas Scaffidi, Clifford W. Hicks, Yoshiteru Maeno, npj Quant Mater 2, 40 (2017). DOI: https://doi.org/10.1038/s41535-017-0045-4

    2017 doi

  24. [32]

    Wen Huang, Chin. Phys. B, 30, 107403 (2021). DOI: 10.1088/1674-1056/ac2488

    2021 doi

  25. [33]

    Leggett, Ying Liu, Journal of Supercon- ductivity and Novel Magnetism 34, 1647 (2021)

    Anthony J. Leggett, Ying Liu, Journal of Supercon- ductivity and Novel Magnetism 34, 1647 (2021). DOI: https://doi.org/10.1007/s10948-020-05717-6

    2021 doi

  26. [34]

    A. P. Mackenzie, R. K. W. Haselwimmer, A. W. Tyler, G. G. Lonzarich, Y. Mori, S. Nishizaki, Y. Maeno, Phys. Rev. Lett. 80, 161 (1998); [Er- ratum Phys. Rev. Lett. 80, 3890 (1998)]. DOI: https://doi.org/10.1103/PhysRevLett.80.161

    1998 doi

  27. [35]

    A. P. Mackenzie, S. R. Julian, A. J. Diver, G. J. Mc- Mullan, M. P. Ray, G. G. Lonzarich, Y. Maeno, S. Nishizaki, T. Fujita, Phys. Rev. Lett. 76, 3786 (1996). DOI: https://doi.org/10.1103/PhysRevLett.76.3786

    1996 doi

  28. [36]

    P. J. Curran, S. J. Bending, W. M. Desoky, A. S. Gibbs, S. L. Lee, and A. P. Macken- zie, Phys. Rev. B 89, 144504 (2014) DOI: https://doi.org/10.1103/PhysRevB.89.144504

    2014 doi

  29. [37]

    et al., Sci Rep 13, 12652 (2023)

    Curran, P.J., Bending, S.J., Gibbs, A.S. et al., Sci Rep 13, 12652 (2023). DOI: https://doi.org/10.1038/s41598- 023-39590-9

    2023 doi

  30. [38]

    DOI: https://doi.org/10.1038/s41535-020- 0245-1

    Steven Allan Kivelson, Andrew Chang Yuan, Brad Ramshaw, Ronny Thomale, npj Quantum Materials, 5, 43 (2020). DOI: https://doi.org/10.1038/s41535-020- 0245-1

    2020 doi

  31. [39]

    Hassinger, P

    E. Hassinger, P. Bourgeois-Hope1, H. Taniguchi, S. Ren´ e de Cotret, G. Grissonnanche, M. S. Anwar, Y. Maeno, N. Doiron-Leyraud1, Louis Taillefer, Phys. Rev. X 7, 011032 (2017). DOI: https://doi.org/10.1103/PhysRevX.7.011032

    2017 doi

  32. [40]

    Leggett Rev

    Anthony J. Leggett Rev. Mod. Phys. 47, 331 (1975) [Erratum Rev. Mod. Phys. 48, 357 (1976).] DOI: https://doi.org/10.1103/RevModPhys.47.331

    1975 doi

  33. [41]

    Murakawa, K

    H. Murakawa, K. Ishida, K. Kitagawa, Z. Q. Mao1, Y. Maeno, Phys. Rev. Lett. 93 167004 (2004). DOI: https://doi.org/10.1103/PhysRevLett.93.167004

    2004 doi

  34. [42]

    Annett, Adv

    James F. Annett, Adv. Phys. 39, 83 (1990). https://doi.org/10.1080/00018739000101481

    1990 doi

  35. [43]

    Annett, B

    James F. Annett, B. L. Gy¨ orffy, G. Litak, K. I. Wysoki´ nski, Phys. Rev. B 78, 054511 (2008). DOI: 10.1103/PhysRevB.78.054511

    2008 doi

  36. [45]

    Krieger, Thomas J

    Hisakazu Matsuki, Rustem Khasanov, Jonas A. Krieger, Thomas J. Hicken, Kosuke Yuchi, Jake S. Bobowski, Giordano Mattoni, Atsutoshi Ikeda, Ryutaro Okuma, Hubertus Luetkens, Yoshiteru Maeno, Phys. Rev. Lett. 136, 066001 (2026). DOI: 10.1103/sgcz-9rc7

    2026 doi

  37. [46]

    Gupta, T

    R. Gupta, T. Saunderson, S. Shallcross, M. Gradhand, J. Quintanilla, and J. Annett, Phys. Rev. B bf 102, 235203 (2020). DOI: https://doi.org/10.1103/PhysRevB.102.235203

    2020 doi

  38. [47]

    A. T. Romer, D. D. Scherer, I. M. Eremin, P. J. Hirschfeld, B. M. Andersen, Phys. Rev. Lett.123, 247001 (2019). DOI: 10.1103/PhysRevLett.123.247001

    2019 doi

  39. [48]

    Gupta, S

    R. Gupta, S. Shallcross, J. Quintanilla, M. Gradhand and J. Annett, Phys. Rev. B 106, 115126 (2022) DOI: https://doi.org/10.1103/PhysRevB.106.115126

    2022 doi

  40. [49]

    Phys.: Condens

    Sudeep Kumar Ghosh et al 2021 J. Phys.: Condens. Matter 33 033001. DOI: https://iopscience.iop.org/article/10.1088/1361- 648X/abaa06

    2021 doi

  41. [50]

    Matter4, 47 (2019)

    Karol Izydor Wysoki´ nski, Condens. Matter4, 47 (2019). DOI:10.3390/condmat4020047

    2019 doi

  42. [51]

    Fudamoto,K

    G.Luke, Y. Fudamoto,K. M. Kojima, M. I. Larkin, J. Merrin, B. Nachumi, Y. J. Uemura, Y. Maeno, Z. Q. Mao, Y. Mori, H. Nakamura, M. Sigrist, Time-reversal symmetry-breaking superconductiv- ity in Sr 2RuO4, Nature 394, 558 (1998). DOI: https://doi.org/10.1038/29038

    1998 doi

  43. [52]

    Capelle E

    K. Capelle E. K. U. Gross, B. L. Gy¨ orffy, Phys. Rev. Lett. 78, 3753 (1997). DOI: https://doi.org/10.1103/PhysRevLett.78.3753

    1997 doi

  44. [53]

    Capelle E

    K. Capelle E. K. U. Gross and B. L. Gy¨ orffy Phys. Rev. B 58, 473 (1998) DOI: https://doi.org/10.1103/PhysRevB.58.473

    1998 doi

  45. [54]

    Edward Taylor and Catherine Kallin Phys. Rev. Lett. 108, 157001 (2012). DOI: https://doi.org/10.1103/PhysRevLett.108.157001

    2012 doi

  46. [55]

    K. I. Wysoki´ nski, James F. Annett, and B. L. Gy¨ orffy Phys. Rev. Lett. 108, 077004 (2012). DOI: https://doi.org/10.1103/PhysRevLett.108.077004

    2012 doi

  47. [56]

    Wysokinski, James F

    Martin Gradhand, Karol I. Wysokinski, James F. Annett, and Balazs L. Gy¨ orffy Phys. Rev. B 88, 094504 (2013) DOI: https://doi.org/10.1103/PhysRevB.88.094504

    2013 doi

  48. [57]

    Mineev Phys

    Vladimir P. Mineev Phys. Rev. B 76, 212501 (2007). DOI: https://doi.org/10.1103/PhysRevB.76.212501

    2007 doi

  49. [58]

    Mineev J

    Vladimir P. Mineev J. Phys. Soc. Jpn.81, 093703 (2012). DOI: https://doi.org/10.1143/JPSJ.81.093703

    2012 doi

  50. [59]

    Mineev Phys

    V.P. Mineev Phys. Rev. B 89, 134519 (2014). DOI: https://doi.org/10.1103/PhysRevB.89.134519

    2014 doi

  51. [60]

    Phys.: Con- dens

    Martin Gradhand and James F Annett, J. Phys.: Con- dens. Matter 26, 274205 (2014). DOI: 10.1088/0953- 8984/26/27/274205

    2014 doi

  52. [61]

    Jun Goryo Phys. Rev. B 78, 060501(R) (2008). DOI: https://doi.org/10.1103/PhysRevB.78.060501

    2008 doi

  53. [62]

    Lutchyn, Pavel Nagornykh, and Victor M

    Roman M. Lutchyn, Pavel Nagornykh, and Victor M. Yakovenko Phys. Rev. B 80, 104508 (2009). DOI: https://doi.org/10.1103/PhysRevB.80.104508

    2009 doi

  54. [63]

    K¨ onig and Alex Levchenko Phys

    Elio J. K¨ onig and Alex Levchenko Phys. Rev. Lett. 118, 027001 (2017) DOI: https://doi.org/10.1103/PhysRevLett.118.027001

    2017 doi

  55. [64]

    H. G. Suh, H. Menke, P. M. R. Brydon, C. Timm, A. Ramires and D. F. Agterberg, Phys. Rev. Re- search 2, 032023(R) (2020). DOI: 10.1103/PhysRevRe- search.2.032023

    2020 doi

  56. [65]

    Lange and G

    E. Lange and G. Kotliar, Phys. Rev. Lett. bf 82, 1317 (1999). DOI: https://doi.org/10.1103/PhysRevLett.82.1317

    1999 doi

  57. [66]

    Zhang and H

    Y. Zhang and H. Huang, arXiv:2604.08043 DOI: https://doi.org/10.48550/arXiv.2604.08043

    doi arXiv

  58. [67]

    Grinenko, V., Ghosh, S., Sarkar, R. et al. Nat. Phys. 17, 748–754 (2021). DOI: https://doi.org/10.1038/s41567- 021-01182-7

    2021 doi

Pith tools

Reviewed August 1, 2026 · model on record in the stance chip above.