Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Time-reversal symmetry-breaking charge order in a kagome superconductor

Abstract

The kagome lattice1, which is the most prominent structural motif in quantum physics, benefits from inherent non-trivial geometry so that it can host diverse quantum phases, ranging from spin-liquid phases, to topological matter, to intertwined orders2,3,4,5,6,7,8 and, most rarely, to unconventional superconductivity6,9. Recently, charge sensitive probes have indicated that the kagome superconductors AV3Sb5 (A = K, Rb, Cs)9,10,11 exhibit unconventional chiral charge order12,13,14,15,16,17,18,19, which is analogous to the long-sought-after quantum order in the Haldane model20 or Varma model21. However, direct evidence for the time-reversal symmetry breaking of the charge order remains elusive. Here we use muon spin relaxation to probe the kagome charge order and superconductivity in KV3Sb5. We observe a noticeable enhancement of the internal field width sensed by the muon ensemble, which takes place just below the charge ordering temperature and persists into the superconducting state. Notably, the muon spin relaxation rate below the charge ordering temperature is substantially enhanced by applying an external magnetic field. We further show the multigap nature of superconductivity in KV3Sb5 and that the \({T}_{{\rm{c}}}/{\lambda }_{ab}^{-2}\) ratio (where Tc is the superconducting transition temperature and λab is the magnetic penetration depth in the kagome plane) is comparable to those of unconventional high-temperature superconductors. Our results point to time-reversal symmetry-breaking charge order intertwining with unconventional superconductivity in the correlated kagome lattice.

This is a preview of subscription content, access via your institution

Relevant articles

Open Access articles citing this article.

Access options

Buy article

Get time limited or full article access on ReadCube.

$32.00

All prices are NET prices.

Fig. 1: Indication of time-reversal symmetry-breaking of the charge order in KV3Sb5.
Fig. 2: Enhanced magnetic response of the charge order with applying external magnetic fields.
Fig. 3: Correlated kagome superconductivity.

Data availability

All relevant data are available from the authors. Alternatively, the data can be accessed through the data base at the following link: http://musruser.psi.ch/cgi-bin/SearchDB.cgi.

References

  1. Syôzi, I. Statistics of kagome lattice. Prog. Theor. Phys. 6, 306-308 (1951).

    ADS  MathSciNet  MATH  Google Scholar 

  2. Barz, H. Ternary transition metal phosphides: high-temperature superconductors. Mater. Res. Bull. 15, 1489-1491 (1980).

    CAS  Google Scholar 

  3. Zhou, Y., Kanoda, K. & Ng, T.-K. Quantum spin liquid states. Rev. Mod. Phys. 89, 025003 (2017).

    ADS  MathSciNet  Google Scholar 

  4. Guguchia, Z. et al. Tunable anomalous Hall conductivity through volume-wise magnetic competition in a topological kagome magnet. Nat. Commun. 11, 559 (2020).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  5. Yin, J.-X., Pan, S. H. & Hasan, M. Z. Probing topological quantum matter with scanning tunneling microscopy. Nat. Rev. Phys. 3, 249–263 (2021).

    Google Scholar 

  6. Mielke, III, C. et al. Nodeless kagome superconductivity in LaRu3Si2. Phys. Rev. Materials 5, 034803 (2021).

    ADS  CAS  Google Scholar 

  7. J.-X. Yin, et. al., Quantum-limit Chern topological magnetism in TbMn6Sn6. Nature 583, 533–536 (2020).

    ADS  CAS  PubMed  Google Scholar 

  8. Pershoguba, S. S. & Yakovenko, V. M. Optical control of topological memory based on orbital magnetization. Preprint at http://arxiv.org/abs/2106.01192 (2021).

  9. Ortiz, B. et al. CsV3Sb5: a Z2 topological kagome metal with a superconducting ground state. Phys. Rev. Lett. 125, 247002 (2020).

    ADS  CAS  PubMed  Google Scholar 

  10. Ortiz, B. et al. Superconductivity in the Z2 kagome metal KV3Sb5. Phys. Rev. Materials 5, 034801 (2021).

    ADS  CAS  Google Scholar 

  11. Yin, Q. et al. Superconductivity and normal-state properties of kagome metal RbV3Sb5 single crystals. Chin. Phys. Lett. 38, 037403 (2021).

    ADS  CAS  Google Scholar 

  12. Jiang, Y.-X. et al. Discovery of topological charge order in kagome superconductor KV3Sb5. Nat. Mater. 20, 1353–1357 (2021).

    ADS  CAS  PubMed  Google Scholar 

  13. Shumiya, N. et al. Tunable chiral charge order in kagome superconductor RbV3Sb5. Phys. Rev. B 104, 035131 (2021).

    ADS  CAS  Google Scholar 

  14. Wang, Z. et al. Electronic nature of chiral charge order in the kagome superconductor CsV3Sb5. Phys. Rev. B 104, 075148 (2021).

    ADS  CAS  Google Scholar 

  15. Feng, X., Jiang, K., Wang, Z. & Hu, J. Chiral flux phase in the Kagome superconductor AV3Sb5. Sci. Bull. 66, 1384–1388 (2021).

    CAS  Google Scholar 

  16. Denner, M., Thomale, R. & Neupert, T. Analysis of charge order in the kagome metal AV3Sb5 (A = K, Rb, Cs). Phys. Rev. Lett. 127, 217601 (2021).

    ADS  CAS  PubMed  Google Scholar 

  17. Lin, Y.-P. & Nandkishore, R. Complex charge density waves at Van Hove singularity on hexagonal lattices: Haldane-model phase diagram and potential realization in kagome metals AV3Sb5. Phys. Rev. B 104, 045122 (2021).

    ADS  CAS  Google Scholar 

  18. Wu, X. et al. Nature of unconventional pairing in the kagome superconductors AV3Sb5. Phys. Rev. Lett. 127, 177001 (2021).

    ADS  CAS  PubMed  Google Scholar 

  19. Setty, C., Hu, H., Chen, L. & Si, Q. Electron correlations and T-breaking density wave order in a Z2 kagome metal. Preprint at https://arxiv.org/abs/2105.15204 (2021).

  20. Haldane, F. D. M. Model for a quantum Hall effect without Landau levels: condensed-matter realization of the parity anomaly. Phys. Rev. Lett. 61, 2015–2018 (1988).

    ADS  CAS  PubMed  Google Scholar 

  21. Varma, C. M. Non-Fermi-liquid states and pairing instability of a general model of copper oxide metals. Phys. Rev. B 55, 14554–14580 (1997).

    ADS  CAS  Google Scholar 

  22. Chakravarty, S., Laughlin, R., Morr, D. & Nayak, C. Hidden order in the cuprates. Phys. Rev. B 63, 094503 (2001).

    ADS  Google Scholar 

  23. Yang, S. et al. Giant, unconventional anomalous Hall effect in the metallic frustrated magnet candidate, KV3Sb5. Sci. Adv. 6, eabb6003 (2020).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  24. Sonier, J. E., Brewer, J. H. & Kiefl, R. F. μSR studies of the vortex state in type-II superconductors. Rev. Mod. Phys. 72, 769 (2000).

    ADS  CAS  Google Scholar 

  25. Luke, G. M. et al. Time-reversal symmetry breaking superconductivity in Sr2RuO4. Nature 394, 558-561 (1998).

    ADS  CAS  Google Scholar 

  26. Kenney, E., Ortiz, B., Wang, C., Wilson, S. & Graf, M. Absence of local moments in the kagome metal KV3Sb5 as determined by muon spin spectroscopy. J. Phys. Condens. Matter 33, 235801 (2021).

    ADS  CAS  Google Scholar 

  27. Kubo, R. & Toyabe, T. Magnetic Resonance and Relaxation (North Holland, 1967).

  28. Huang, W. et al. Precision search for magnetic order in the pseudogap regime of La2−xSrxCuO4 by muon spin relaxation. Phys. Rev. B 85, 104527 (2012).

    ADS  Google Scholar 

  29. Singh, A. D. et al. Time-reversal symmetry breaking and multigap superconductivity in the noncentrosymmetric superconductor La7Ni3. Phys. Rev. B 103, 174502 (2021).

    ADS  Google Scholar 

  30. Sedlak, K., Scheuermann, R., Stoykov, A. & Amato, A. GEANT4 simulation and optimisation of the high-field μSR spectrometer. Physica B 404, 970–973 (2009).

    ADS  CAS  Google Scholar 

  31. Xiang, Y. et al. Twofold symmetry of c-axis resistivity in topological kagome superconductor CsV3Sb5 with in-plane rotating magnetic field. Preprint at https://arxiv.org/abs/2104.06909 (2021).

  32. Zhao, H. et al. Cascade of correlated electron states in a kagome superconductor CsV3Sb5. Preprint at https://arxiv.org/pdf/2103.03118 (2021).

  33. Khasanov, R. et al. Evolution of two-gap behavior of the superconductor FeSe1−x. Phys. Rev. Lett. 104, 087004 (2010).

    ADS  CAS  PubMed  Google Scholar 

  34. Kogan, V. G., Martin, C. & Prozorov, R. Superfluid density and specific heat within a self-consistent scheme for a two-band superconductor. Phys. Rev. B 80, 014507 (2009).

    ADS  Google Scholar 

  35. Gupta, R. et al. Microscopic evidence for anisotropic multigap superconductivity in the CsV3Sb5 kagome superconductor. Preprint at https://arxiv.org/abs/2108.01574 (2021).

  36. Han-Shu, X. et al. Multiband superconductivity with sign-preserving order parameter in kagome superconductor CsV3Sb5. Preprint at https://arxiv.org/pdf/2104.08810.pdf (2021).

  37. Uemura, Y. J. et al. Universal correlations between Tc and ns/m* (carrier density over effective mass) in high-Tc cuprate superconductors. Phys. Rev. Lett. 62, 2317 (1989).

    ADS  CAS  PubMed  Google Scholar 

  38. von Rohr, F. O. et al. Unconventional scaling of the superfluid density with the critical temperature in transition metal dichalcogenides. Sci. Adv. 5, eaav8465 (2019).

    ADS  Google Scholar 

  39. Shengelaya, A. et al. Muon-spin-rotation measurements of the penetration depth of the infinite-layer electron-doped Sr0.9La0.1CuO2 cuprate superconductor. Phys. Rev. Lett. 94, 127001 (2005).

    ADS  CAS  PubMed  Google Scholar 

  40. Luetkens, H. et al. The electronic phase diagram of the LaO1−xFxFeAs superconductor. Nat. Mater. 8, 305-309 (2009).

    ADS  CAS  PubMed  Google Scholar 

  41. Amato, A. et al. The new versatile general purpose surface-muon instrument (GPS) based on silicon photomultipliers for μSR measurements on a continuous-wave beam. Rev. Sci. Instrum. 88, 093301 (2017).

    ADS  CAS  PubMed  Google Scholar 

  42. Suter, A. and Wojek, B. M. Musrfit: a free platform-independent framework for μSR data analysis. Phys. Procedia 30, 69 (2012).

    ADS  CAS  Google Scholar 

  43. Kiesel, M. L. & Thomale, R. Sublattice interference in the kagome Hubbard model. Phys. Rev. B 86, 121105 (2012).

    ADS  Google Scholar 

  44. Lee, S. L. et al. Evidence for two-dimensional thermal fluctuations of the vortex structure in Bi2.15Sr1.85CaCu2O8 + Δ from muon spin rotation experiments. Phys. Rev. Lett. 75, 922 (1995).

    ADS  CAS  PubMed  Google Scholar 

  45. Guguchia, Z. et al. Signatures of the topological s+− superconducting order parameter in the type-II Weyl semimetal Td-MoTe2. Nat. Commun. 8, 1082 (2017).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  46. Brandt, E. H. Flux distribution and penetration depth measured by muon spin rotation in high-Tc superconductors. Phys. Rev. B 37, 2349 (1988).

    ADS  CAS  Google Scholar 

  47. Bouquet, F. et al. Phenomenological two-gap model for the specific heat of MgB2. Europhys. Lett. 56, 856 (2001).

    ADS  CAS  Google Scholar 

  48. Prozorov, R. & Giannetta, R. W. Magnetic penetration depth in unconventional superconductors. Supercond. Sci. Technol. 19, R41 (2006).

    ADS  CAS  Google Scholar 

  49. Khasanov, R. et al. Experimental evidence for two gaps in the high-temperature La1.83Sr0.17CuO4 superconductor. Phys. Rev. Lett. 98, 057007 (2007).

    ADS  CAS  PubMed  Google Scholar 

  50. Khasanov, R. et al. SrPt3P: a two-band single-gap superconductor. Phys. Rev. B 90, 140507(R) (2014).

    ADS  Google Scholar 

  51. Kogan, V. G. London approach to anisotropic type-II superconductors. Phys. Rev. B 24, 1572 (1981).

    ADS  Google Scholar 

  52. Gupta, R. et al. Self-consistent two-gap approach in studying multi-band superconductivity in NdFeAsO0.65F0.35. Front. Phys. 8, 2 (2020).

    Google Scholar 

Download references

Acknowledgements

The μSR experiments were carried out at the Swiss Muon Source (SμS) Paul Scherrer Institute, Villigen, Switzerland. The magnetization measurements were carried out on the MPMS device of the Laboratory for Multiscale Materials Experiments, Paul Scherrer Institute, Villigen, Switzerland (SNSF grant no. 206021_139082). Z.G. acknowledges the useful discussions with R. Scheuermann and A. Amato. Z.G., C.M.III and D.D. thank C. Baines for the technical assistance during DOLLY experiments. M.Z.H. acknowledges visiting scientist support from IQIM at the California Institute of Technology. Experimental and theoretical work at Princeton University was supported by the Gordon and Betty Moore Foundation (GBMF4547 and GBMF9461; M.Z.H.) and the material characterization is supported by the US Department of Energy under the Basic Energy Sciences programme (grant no. DOE/BES DE-FG-02-05ER46200). The theory work at Rice has primarily been supported by the US Department of Energy, BES under award no. DE-SC0018197 and has also been supported by the Robert A. Welch Foundation grant no. C-1411 (Q.S.). The work at Rice university is also supported by US Department of Energy, BES under Grant No. DE-SC0012311 (P.D.). This work is also supported by the Beijing Natural Science Foundation (grant no. Z180008, Z200005), the National Key Research and Development Program of China (grant no. 2017YFA0302900, Y2018YFE0202600) and the National Natural Science Foundation of China (grant no. U2032204). The work of R.G. was supported by the Swiss National Science Foundation (SNF grant no. 200021_175935). T.N. acknowledges funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (ERC-StG-Neupert-757867-PARATOP). H. M. was sponsored by the US Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division. R.T. was supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through Project-ID 258499086-SFB1170 and by the Wurzburg-Dresden Cluster of Excellence on Complexity and Topology in Quantum Matter-ct.qmat Project-ID 390858490-EXC 2147.

Author information

Authors and Affiliations

Authors

Contributions

Z.G., Y.-X.J. and M.Z.H. conceived the study. Z.G. supervised the project. Sample growth and single-crystal X-ray diffraction experiments were carried out by H. Liu and Y.S. Magnetization and Laue X-ray diffraction experiments were performed by C.M.III, Z.G., M.M. and H.C.L. μSR experiments and corresponding discussions were carried out by Z.G., C.M.III, D.D., R.G., R.K., H.Luet., J.J.C., J.-X.Y., Y.-X.J., M.Z.H., X.W., P.D., Q.S., H.M., R.T. and T.N. μSR data analysis was undertaken by Z.G. and C.M.III, with contributions from R.K., H.L., D.D. and R.G. STM experiments were performed by J.-X.Y., Y.-X.J. and M.Z.H. Figure development and the writing of the paper were carried out by Z.G. and C.M.III, with contributions from J.-X.Y., H.Luet. and M.Z.H.  All authors discussed the results, interpretation and conclusion.

Corresponding authors

Correspondence to M. Z. Hasan or Z. Guguchia.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature thanks Victor Yakovenko and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data figures and tables

Extended Data Fig. 1 Crystal structure of KV3Sb5.

Three dimensional representation (a) and top view (b) of the atomic structure of KV3Sb5. In panel (c) is displayed an optical microscope image of a 3 × 2 × 0.2 mm single crystal of KV3Sb5 on millimeter paper, with the scale shown. The hexagonal symmetry is immediately apparent. (d) Scanning Transmission Microscope (STM) image of the V kagome lattice from a cryogenically cleaved sample.

Extended Data Fig. 2 Single Crystal X-Ray Diffraction for KV3Sb5.

(a) X-ray diffraction image for KV3Sb5 recorded at 300 K. The well-defined peaks are labeled with their crystallographic indices. No second phase has been detected. (b) Laue X-ray diffraction image of the single crystal sample KV3Sb5, oriented with the c-axis along the beam. (c) The temperature dependence of magnetic susceptibility of KV3Sb5 above 1.8 K. It shows an anomaly at T* 80 K, coinciding with emergence of a charge order.

Extended Data Fig. 3 Anisotropic magnetic response across charge order temperature in the single crystalline sample of KV3Sb5.

(a) The temperature dependence of magnetic susceptibility for KV3Sb5 measured at various magnetic fields applied parallel to the c-axis. (b) The temperature dependence of magnetic susceptibility for KV3Sb5 measured in the field of 1 T, applied both parallel to the kagome plane and parallel to the c-axis.

Extended Data Fig. 4 Zero-field μSR experiment for the single crystalline sample of KV3Sb5.

The ZF μSR time spectra for KV3Sb5, obtained at T = 5 K from detectors 3 & 4 and 2 & 1. The solid curves represent fits to the recorded time spectra, using only Gaussian Kubo Toyabe (GKT) function (red) and the one with an additional exponential exp(−Γt) term (blue). The inset shows the low time part of the spectrum.

Extended Data Fig. 5 Zero-field μSR experiment for the polycrystalline sample of KV3Sb5.

The ZF μSR time spectra for the polycrystalline sample of KV3Sb5, obtained at T = 5 K. The solid curves represent fits to the recorded time spectra, using only Gaussian Kubo Toyabe (GKT) function (red) and the one with an additional exponential exp(−Γt) term (blue). The inset shows the low time part of the spectrum.

Extended Data Fig. 6 High-field μSR experiment for KV3Sb5.

Fourier transform for the μSR asymmetry spectra of KV3Sb5 at 5 K for the applied field of μ0H = 8 T. The black solid line represents the fit to the data using the two component signal. Red and blue solid lines show the signals arising from the sample and the silver sample holder (majority), respectively. The inset shows the temperature dependences of the muon spin relaxation rates arising from the sample and the silver sample holder.

Extended Data Fig. 7 Superconducting gap symmetry in KV3Sb5.

(a) The SC muon depolarization rates σSC,ab, and σSC,ac as well as the inverse squared magnetic penetration depth \({\lambda }_{ab}^{-2}\) and \({\lambda }_{ac}^{-2}\) as a function of temperature, measured in 5 mT, applied parallel and perpendicular to the kagome plane. (b) The SC muon depolarization rate σSC,ac, measured in 10 mT, applied parallel to the kagome plane. The solid line represents the indistinguishable 2-gap s-wave and s + d wave model. The error bars represent the s.d. of the fit parameters. (c) Temperature dependence of the difference between the internal field μ0HSC measured in the SC state and the one measured in the normal state μ0HNS at T = 5 K for KV3Sb5.

Extended Data Fig. 8 A self-consistent approach for a two-band superconductor in KV3Sb5.

The SC muon depolarization rates σSC,c (a), and σSC,ab (b) as a function of temperature, measured in 5 mT, applied perpendicular and parallel to the kagome plane. (c) The SC muon depolarization rate σSC,ac, measured in 10 mT, applied parallel to the kagome plane. The solid black and purple lines are the theoretical curves obtained within the framework of self-consistent approach for a two-band superconductor described in the text. The red and the blue dashed lines correspond to the contribution of the large and the small superconducting gaps to the total superfluid density, solid black lines. The insets show the temperature dependences of the large Δ1 and the small Δ2.

Extended Data Table 1 Atomic positions
Extended Data Table 2 Crystallographic refinement

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Mielke, C., Das, D., Yin, JX. et al. Time-reversal symmetry-breaking charge order in a kagome superconductor. Nature 602, 245–250 (2022). https://doi.org/10.1038/s41586-021-04327-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41586-021-04327-z

Further reading

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing