Skip to main content

Thank you for visiting 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.

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


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.

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.


All prices are NET prices.

Fig. 1: Three-state nematic order in RbV3Sb5.
Fig. 2: Three-state nematic order in KV3Sb5 and CsV3Sb5.
Fig. 3: MOKE in AV3Sb5.
Fig. 4: CD in AV3Sb5.

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.


  1. Han, T. H. et al. Fractionalized excitations in the spin-liquid state of a kagome-lattice antiferromagnet. Nature 492, 406–410 (2012).

    Article  ADS  Google Scholar 

  2. Nakatsuji, S., Kiyohara, N. & Higo, T. Large anomalous Hall effect in a non-collinear antiferromagnet at room temperature. Nature 527, 212–215 (2015).

    Article  ADS  Google Scholar 

  3. Belopolski, I. et al. Discovery of topological Weyl fermion lines and drumhead surface states in a room temperature magnet. Science 365, 1278–1281 (2019).

  4. Yin, J. X. et al. Giant and anisotropic many-body spin–orbit tunability in a strongly correlated kagome magnet. Nature 562, 91–95 (2018).

  5. Yin, J. X. et al. Negative flat band magnetism in a spin–orbit-coupled correlated kagome magnet. Nat. Phys. 15, 443–448 (2019).

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

    Article  ADS  Google Scholar 

  7. Ye, L. et al. Massive Dirac fermions in a ferromagnetic kagome metal. Nature 555, 638–642 (2018).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  9. Lin, Y.-P. & Nandkishore, R. M. Complex charge density waves at van Hove singularity on hexagonal lattices: Haldane-model phase diagram and potential realization in the kagome metals AV3Sb5 (A = K, Rb, Cs). Phys. Rev. B 104, 045122 (2021).

  10. Park, T., Ye, M. & Balents, L. Electronic instabilities of kagome metals: Saddle points and Landau theory. Phys. Rev. B 104, 035142 (2021).

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

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

    Article  ADS  Google Scholar 

  13. Ortiz, B. R. et al. New kagome prototype materials: discovery of KV3 Sb5, RbV3 Sb5, and CsV3 Sb5. Phys. Rev. Mater. 3, 094407 (2019).

  14. Ortiz, B. R. et al. CsV Sb : a \(\Bbb{Z}_2\) topological kagome metal with a superconducting ground state. Phys. Rev. Lett. 125, 247002 (2020).

  15. Ortiz, B. R. et al. Superconductivity in the \(\Bbb{Z}_2\) kagome metal KV Sb. Phys. Rev. Mater. 5, 034801 (2021).

  16. Jiang, Y. X. et al. Unconventional chiral charge order in kagome superconductor KV3Sb5. Nat. Mater. 20, 1353–1357 (2021).

    Article  ADS  Google Scholar 

  17. Xu, H.-S. et al. Multiband superconductivity with sign-preserving order parameter in kagome superconductor CsV3Sb5. Phys. Rev. Lett. 127, 187004 (2021).

    Article  ADS  Google Scholar 

  18. Liu, Z. et al. Charge-density-wave-induced bands renormalization and energy gaps in a kagome superconductor RbV3Sb5. Phys. Rev. X 11, 041010 (2021).

    Google Scholar 

  19. Shumiya, N. et al. Intrinsic nature of chiral charge order in the kagome superconductor RbV3Sb5. Phys. Rev. B 104, 035131 (2021).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  21. Wang, Q. et al. Charge density wave orders and enhanced superconductivity under pressure in the kagome metal CsV3Sb5. Adv. Mater. 33, 2102813 (2021).

    Article  Google Scholar 

  22. Lou, R. et al. Charge-density-wave-induced peak–dip–hump structure and the multiband superconductivity in a kagome superconductor CsV3Sb5. Phys. Rev. Lett. 128, 036402 (2022).

    Article  ADS  Google Scholar 

  23. Chen, H. et al. Roton pair density wave in a strong-coupling kagome superconductor. Nature 599, 222–228 (2021).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  25. Mielke, C. et al. Time-reversal symmetry-breaking charge order in a kagome superconductor. Nature 602, 245–250 (2022).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  27. Yu, F. H. et al. Concurrence of anomalous hall effect and charge density wave in a superconducting topological kagome metal. Phys. Rev. B 104, L041103 (2021).

    Article  ADS  Google Scholar 

  28. Li, H. et al. Rotation symmetry breaking in the normal state of a kagome superconductor KV3Sb5. Nat. Phys. 18, 265–270 (2022).

    Article  Google Scholar 

  29. Ortiz, B. R. et al. Fermi surface mapping and the nature of charge-density-wave order in the kagome superconductor CsV3Sb5. Phys. Rev. X 11, 041030 (2021).

    Google Scholar 

  30. Wu, Q. et al. The large static and pump-probe Kerr effect with two-fold rotation symmetry in kagome metal CsV3Sb5. Preprint at arXiv:2110.11306 (2021).

  31. Zhao, H. et al. Cascade of correlated electron states in the kagome superconductor CsV3Sb5. Nature 599, 216–221 (2021).

    Article  ADS  Google Scholar 

  32. Xiang, Y. et al. Twofold symmetry of c-axis resistivity in topological kagome superconductor CsV3Sb5 with in-plane rotating magnetic field. Nat. Commun. 12, 6727 (2021).

    Article  ADS  Google Scholar 

  33. Ni, S. et al. Anisotropic superconducting properties of kagome metal CsV3Sb5. Chin. Phys. Lett. 38, 057403 (2021).

    Article  ADS  Google Scholar 

  34. Nie, L. et al. Charge-density-wave-driven electronic nematicity in a kagome superconductor. Nature 604, 59–64 (2022).

    Article  ADS  Google Scholar 

  35. Choi, T. et al. Insulating interlocked ferroelectric and structural antiphase domain walls in multiferroic YMnO3. Nat. Mater. 9, 253–258 (2010).

    Article  ADS  Google Scholar 

  36. Luo, J. et al. Possible star-of-David pattern charge density wave with additional modulation in the kagome superconductor CsV3Sb5. npj Quantum Mater. 7, 30 (2022).

    Article  ADS  Google Scholar 

  37. Mu, C. et al. s-wave superconductivity in kagome metal CsV3Sb5 revealed by 121/123Sb NQR and 51V NMR measurements. Chin. Phys. Lett. 38, 077402 (2021).

    Article  ADS  Google Scholar 

  38. Song, D. et al. Orbital ordering and fluctuations in a kagome superconductor CsV3Sb5. Sci. China Phys., Mech. Astron. 65, 247462 (2022).

    Article  ADS  Google Scholar 

  39. Ni, Z. et al. Direct imaging of antiferromagnetic domains and anomalous layer-dependent mirror symmetry breaking in atomically thin MnPS3. Phys. Rev. Lett. 127, 187201 (2021).

    Article  ADS  Google Scholar 

  40. Ni, Z. et al. Imaging the Néel vector switching in the monolayer antiferromagnet MnPSe3 with strain-controlled Ising order. Nat. Nanotechnol. 16, 782–787 (2021).

    Article  ADS  Google Scholar 

  41. Zhou, X. et al. Origin of charge density wave in the kagome metal CsV3Sb5 as revealed by optical spectroscopy. Phys. Rev. B 104, L041101 (2021).

    Article  ADS  Google Scholar 

  42. Uykur, E., Ortiz, B. R., Wilson, S. D., Dressel, M. & Tsirlin, A. A. Optical detection of the density-wave instability in the kagome metal KV3Sb5. npj Quantum Mater. 7, 16 (2022).

    Article  ADS  Google Scholar 

  43. Liang, Z. et al. Three-dimensional charge density wave and surface-dependent vortex-core states in a kagome superconductor CsV3Sb5. Phys. Rev. X 11, 031026 (2021).

    Google Scholar 

  44. Miao, H. et al. Geometry of the charge density wave in the kagome metal AV3Sb5. Phys. Rev. B 104, 195132 (2021).

    Article  ADS  Google Scholar 

  45. Ratcliff, N., Hallett, L., Ortiz, B. R., Wilson, S. D. & Harter, J. W. Coherent phonon spectroscopy and interlayer modulation of charge density wave order in the kagome metal CsV3Sb5. Phys. Rev. Mater. 5, L111801 (2021).

    Article  ADS  Google Scholar 

  46. Li, H. et al. Observation of unconventional charge density wave without acoustic phonon anomaly in kagome superconductors AV3Sb5 (A = Rb, Cs). Phys. Rev. X 11, 031050 (2021).

    Google Scholar 

  47. Kang, M. et al. Twofold van Hove singularity and origin of charge order in topological kagome superconductor CsV3Sb5. Nat. Phys. 18, 301–308 (2022).

    Article  Google Scholar 

  48. Luo, H. et al. Electronic nature of charge density wave and electron–phonon coupling in kagome superconductor KV3Sb5. Nat. Commun. 13, 273 (2022).

    Article  ADS  Google Scholar 

  49. Nakayama, K. et al. Carrier injection and manipulation of charge-density wave in kagome superconductor CsV3Sb5. Phys. Rev. X 12, 011001 (2022).

    Google Scholar 

  50. Nakayama, K. et al. Multiple energy scales and anisotropic energy gap in the charge-density-wave phase of the kagome superconductor CsV3Sb5. Phys. Rev. B 104, L161112 (2021).

    Article  ADS  Google Scholar 

  51. Kiesel, M. L., Platt, C. & Thomale, R. Unconventional Fermi surface instabilities in the kagome Hubbard model. Phys. Rev. Lett. 110, 126405 (2013).

    Article  ADS  Google Scholar 

  52. Christensen, M., Birol, T., Andersen, B. & Fernandes, R. Theory of the charge density wave in AV3Sb5 kagome metals. Phys. Rev. B 104, 214513 (2021).

    Article  ADS  Google Scholar 

  53. Tan, H., Liu, Y., Wang, Z. & Yan, B. Charge density waves and electronic properties of superconducting kagome metals. Phys. Rev. Lett. 127, 046401 (2021).

    Article  ADS  Google Scholar 

  54. Higo, T. et al. Large magneto-optical Kerr effect and imaging of magnetic octupole domains in an antiferromagnetic metal. Nat. Photonics 12, 73–78 (2018).

    Article  ADS  Google Scholar 

Download references


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 and Affiliations



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.

Additional information

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.

Rights and permissions

Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

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).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:

This article is cited by


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