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# Three-state nematicity and magneto-optical Kerr effect in the charge density waves in kagome superconductors

## Abstract

The kagome lattice provides a fascinating playground to study geometrical frustration, topology and strong correlations. The newly discovered kagome metals AV3Sb5 (where A can refer to K, Rb or Cs) exhibit phenomena including topological band structure, symmetry-breaking charge-density waves and superconductivity. Nevertheless, the nature of the symmetry breaking in the charge-density wave phase is not yet clear, despite the fact that it is crucial in order to understand whether the superconductivity is unconventional. In this work, we perform scanning birefringence microscopy on all three members of this family and find that six-fold rotation symmetry is broken at the onset of the charge-density wave transition in all these compounds. We show that the three nematic domains are oriented at 120° to each other and propose that staggered charge-density wave orders with a relative π phase shift between layers is a possibility that can explain these observations. We also perform magneto-optical Kerr effect and circular dichroism measurements. The onset of both signals is at the transition temperature, indicating broken time-reversal symmetry and the existence of the long-sought loop currents in that phase.

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Nature Communications Open Access 26 November 2022

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## Data availability

All data needed to evaluate the conclusions in the paper are present in the paper and the extended data figures. Additional data related to this paper can be requested from the authors. Source data are provided with this paper.

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## Acknowledgements

We thank C. Varma, Z. Wang and I. Zeljkovic for helpful discussions. This project is mainly supported by L.W.’s startup package at the University of Pennsylvania. The development of the imaging systems was sponsored by the Army Research Office and was accomplished under grants no. W911NF-21-1-0131, W911NF-20-2-0166 and W911NF-19-1-0342, and the Vice Provost for Research University Research Foundation. Y.X. is also partially supported by the NSF EAGER grant via the CMMT programme (DMR-2132591), a seed grant from NSF-funded Penn MRSEC (DMR-1720530) and the Gordon and Betty Moore Foundation’s EPiQS Initiative, and grant GBMF9212 to L.W.. Z.N. acknowledges support from the Vagelos Institute of Energy Science and Technology graduate fellowship and the Dissertation Completion Fellowship at the University of Pennsylvania. B.R.O. and S.D.W. acknowledge support via the UC Santa Barbara NSF Quantum Foundry funded via the Q-AMASE-i program under award DMR-1906325. Q.D. is partially supported by the NSF EPM program under grant no. DMR-2213891. B.Y. acknowledges funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (ERC Consolidator Grant ‘NonlinearTopo’, no. 815869). L.B. is supported by the NSF CMMT program under grant no. DMR-2116515. L.W. acknowledges the support by the Air Force Office of Scientific Research under award no. FA9550-22-1-0410.

## Author information

Authors

### Contributions

L.W. conceived and supervised the project. Y.X. performed the experiments and analysed the data with Z.N., Q.D. and L.W.. Y.L. and B.Y. performed the CD symmetry analysis. B.R.O. and S.D.W. grew the crystals. L.W., Y.X., S.D.W., B.Y. and L.B. discussed and interpreted the data. L.W. and Y.X. wrote the manuscript with input from all authors. All authors edited the manuscript.

### Corresponding author

Correspondence to Liang Wu.

## Ethics declarations

### Competing interests

The authors declare no competing financial interests.

## Peer review

### Peer review information

Nature Physics thanks Turan Birol, Hu Miao and Luyi Yang for their contribution to the peer review of this work.

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

## Extended data

### Extended Data Fig. 1 Additional measurements on three-state nematic order and MOKE in RbV3Sb5.

a, 3D lattice structures showing two other possible staggered CDW orders with a π phase shift, the staggered star-of-David (SoD) and the staggered alternating star-of-David (SoD) and tri-hexgonal (TrH) CDW orders. b, Optical image of the mapping region in Fig. 1(f) in RbV3Sb5. The black dots indicate impurities on the surface. c, θT vs temperature for various incident polarization measured in region 2 in RbV3Sb5. d, MOKE signal vs temperature measured at the zero birefringence incident angle in region 2 in RbV3Sb5. The error bar is 3.7 μRad (see main text for definition of error). eg, Polar plots of the birefringence patterns at T = 70 K measured at the corresponding spots in region 4, 5 and 6 (see Fig. 1(f)), respectively.

### Extended Data Fig. 2 θT vs temperature and characterization of the Cs sample in the main text.

a, θT vs temperature for various incident polarization for the Cs sample shown in b,c in this figure, which is also the same sample for Fig. 2-4 in the main text and Extended data Fig.6-8. The sharp transition in θT at certain polarization is more consistent with a first order transition in the Cs sample, which is consistent with NMR/NQR measurements. Note that the Cs sample in extended data Fig.3 is a different sample, which shows a smoother transition. b, Mapping of the normalized I(0f) signal, the reflectivity, in the CsV3Sb5 sample. A variation of the I(0f) signal is observed in the mapping data, which indicates an uneven surface. c, Optical image of the cleaved Cs sample, the red box indicates the mapping region in b.

### Extended Data Fig. 3 Dependence of θT on temperature and incident polarization of K and Cs compound.

a,c, θT vs temperature for various incident polarization for KV3Sb5 and CsV3Sb5, respectively. b,d, θT vs incident polarization at different temperature cuts for KV3Sb5 and CsV3Sb5, respectively.

### Extended Data Fig. 4 Temperature dependent MOKE at ϕ0 and ϕ0 ± 0.8.

ac, MOKE signal measured at the incident angles ϕ0 = 3. 6 and ϕ0 ± 0.8 in region 5 for RbV3Sb5, where ϕ0 is the incident angle that birefringence contribution is zero. The error bar is defined as the statistical error for data points averaged together over 2 K range bins.

### Extended Data Fig. 5 Birefringence domains under thermal cycles.

a,b, Spatial mapping of θT at T = 6 K, before and after thermal cycles for RbV3Sb5.

### Extended Data Fig. 6 Circular dichroism maps of AV3Sb5.

ac, Circular dichroism maps at T= 6 K for Rb, Cs and K compounds, respectively. The red and green star symbols indicate the positions where circular dichroism vs temperature measurements are performed in Fig. 4.

### Extended Data Fig. 7 Second harmonic generation of AV3Sb5.

ac, Second harmonic generation vs temperature for Rb, Cs and K compounds, respectively. The error bar is defined as the statistical error for data points averaged together over 5 K range bins.

### Extended Data Fig. 8 Comparison of birefringence and circular dichroism maps of CsV3Sb5.

a,b, The spatial birefringence and circular dichroism maps of CsV3Sb5 at T = 6 K, respectively. The region circled by red is region 2, where points within each region have the same birefringence pattern. The green and black dots indicate two spots in R2 (S1 and S2), which have same birefringence patterns but opposite signs of CD signal. c, Histograms of circular dichroism signals within region 2. Both positive and negative CD signals exist within R2. d, θT vs incident polarization at T= 70 K measured at S1 and S2 within R2, respectively.

### Extended Data Fig. 9 Optical set-ups in this paper.

a,b, Optical set-ups for the birefringence (a) and circular dichroism (b) measurements.

## Source data

### Source Data Fig. 1

Statistical source data showing three-state nematic order in RbV3Sb5.

### Source Data Fig. 2

Statistical source data showing three-state nematic order in KV3Sb5 and CsV3Sb5.

### Source Data Fig. 3

Statistical source data for MOKE in AV3Sb5.

### Source Data Fig. 4

Statistical source data for CD in AV3Sb5.

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Xu, Y., Ni, Z., Liu, Y. et al. Three-state nematicity and magneto-optical Kerr effect in the charge density waves in kagome superconductors. Nat. Phys. 18, 1470–1475 (2022). https://doi.org/10.1038/s41567-022-01805-7

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• DOI: https://doi.org/10.1038/s41567-022-01805-7

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