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# 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.

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## Relevant articles

• ### Two types of charge order with distinct interplay with superconductivity in the kagome material CsV3Sb5

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## 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

### 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.

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

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## 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.

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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

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

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