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.

# Cascade of correlated electron states in the kagome superconductor CsV3Sb5

## Abstract

The kagome lattice of transition metal atoms provides an exciting platform to study electronic correlations in the presence of geometric frustration and nontrivial band topology1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18, which continues to bear surprises. Here, using spectroscopic imaging scanning tunnelling microscopy, we discover a temperature-dependent cascade of different symmetry-broken electronic states in a new kagome superconductor, CsV3Sb5. We reveal, at a temperature far above the superconducting transition temperature Tc ~ 2.5 K, a tri-directional charge order with a 2a0 period that breaks the translation symmetry of the lattice. As the system is cooled down towards Tc, we observe a prominent V-shaped spectral gap opening at the Fermi level and an additional breaking of the six-fold rotational symmetry, which persists through the superconducting transition. This rotational symmetry breaking is observed as the emergence of an additional 4a0 unidirectional charge order and strongly anisotropic scattering in differential conductance maps. The latter can be directly attributed to the orbital-selective renormalization of the vanadium kagome bands. Our experiments reveal a complex landscape of electronic states that can coexist on a kagome lattice, and highlight intriguing parallels to high-Tc superconductors and twisted bilayer graphene.

This is a preview of subscription content

## Access options

\$32.00

All prices are NET prices.

## Data availability

The data supporting the findings of this study are available upon request from the corresponding author. Source data are provided with this paper.

## Code availability

The computer code used for data analysis is available upon request from the corresponding author.

## References

1. 1.

Sachdev, S. Kagome- and triangular-lattice Heisenberg antiferromagnets: ordering from quantum fluctuations and quantum-disordered ground states with unconfined bosonic spinons. Phys. Rev. B 45, 12377–12396 (1992).

2. 2.

Mazin, I. I. et al. Theoretical prediction of a strongly correlated Dirac metal. Nat. Commun. 5, 4261 (2014).

3. 3.

Guo, H.-M. & Franz, M. Topological insulator on the kagome lattice. Phys. Rev. B 80, 113102 (2009).

4. 4.

Bilitewski, T. & Moessner, R. Disordered flat bands on the kagome lattice. Phys. Rev. B 98, 235109 (2018).

5. 5.

Balents, L., Fisher, M. P. A. & Girvin, S. M. Fractionalization in an easy-axis kagome antiferromagnet. Phys. Rev. B 65, 224412 (2002).

6. 6.

Neupert, T., Santos, L., Chamon, C. & Mudry, C. Fractional quantum Hall states at zero magnetic field. Phys. Rev. Lett. 106, 236804 (2011).

7. 7.

Plat, X., Alet, F., Capponi, S. & Totsuka, K. Magnetization plateaus of an easy-axis kagome antiferromagnet with extended interactions. Phys. Rev. B 92, 174402 (2015).

8. 8.

Wen, J., Rüegg, A., Wang, C.-C. J. & Fiete, G. A. Interaction-driven topological insulators on the kagome and the decorated honeycomb lattices. Phys. Rev. B 82, 075125 (2010).

9. 9.

Yu, S.-L. & Li, J.-X. Chiral superconducting phase and chiral spin-density-wave phase in a Hubbard model on the kagome lattice. Phys. Rev. B 85, 144402 (2012).

10. 10.

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

11. 11.

Sun, K., Gu, Z., Katsura, H. & Das Sarma, S. Nearly flatbands with nontrivial topology. Phys. Rev. Lett. 106, 236803 (2011).

12. 12.

Tang, E., Mei, J.-W. & Wen, X.-G. High-temperature fractional quantum Hall states. Phys. Rev. Lett. 106, 236802 (2011).

13. 13.

O’Brien, A., Pollmann, F. & Fulde, P. Strongly correlated fermions on a kagome lattice. Phys. Rev. B 81, 235115 (2010).

14. 14.

Rüegg, A. & Fiete, G. A. Fractionally charged topological point defects on the kagome lattice. Phys. Rev. B 83, 165118 (2011).

15. 15.

Yan, S., Huse, D. A. & White, S. R. Spin-liquid ground state of the S = 1/2 kagome Heisenberg antiferromagnet. Science 332, 1173–1176 (2011).

16. 16.

Isakov, S. V., Wessel, S., Melko, R. G., Sengupta, K. & Kim, Y. B. Hard-core bosons on the kagome lattice: valence-bond solids and their quantum melting. Phys. Rev. Lett. 97, 147202 (2006).

17. 17.

Wang, W.-S., Li, Z.-Z., Xiang, Y.-Y. & Wang, Q.-H. Competing electronic orders on kagome lattices at van Hove filling. Phys. Rev. B 87, 115135 (2013).

18. 18.

Jiang, H.-C., Devereaux, T. & Kivelson, S. A. Holon Wigner crystal in a lightly doped kagome quantum spin liquid. Phys. Rev. Lett. 119, 067002 (2017).

19. 19.

Wang, Q. et al. Large intrinsic anomalous Hall effect in half-metallic ferromagnet Co3Sn2S2 with magnetic Weyl fermions. Nat. Commun. 9, 3681 (2018).

20. 20.

Morali, N. et al. Fermi-arc diversity on surface terminations of the magnetic Weyl semimetal Co3Sn2S2. Science 365, 1286–1291 (2019).

21. 21.

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

22. 22.

Jiao, L. et al. Signatures for half-metallicity and nontrivial surface states in the kagome lattice Weyl semimetal Co3Sn2S2. Phys. Rev. B 99, 245158 (2019).

23. 23.

Liu, E. et al. Giant anomalous Hall effect in a ferromagnetic kagome-lattice semimetal. Nat. Phys. 14, 1125–1131 (2018).

24. 24.

Lin, Z. et al. Dirac fermions in antiferromagnetic FeSn kagome lattices with combined space inversion and time-reversal symmetry. Phys. Rev. B 102, 155103 (2020).

25. 25.

Kang, M. et al. Dirac fermions and flat bands in the ideal kagome metal FeSn. Nat. Mater. 19, 163–169 (2020).

26. 26.

Lin, Z. et al. Flatbands and emergent ferromagnetic ordering in Fe3Sn2 kagome lattices. Phys. Rev. Lett. 121, 096401 (2018).

27. 27.

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

28. 28.

Ortiz, B. R. et al. New kagome prototype materials: discovery of KV3Sb5, RbV3Sb5, and CsV3Sb5. Phys. Rev. Mater. 3, 094407 (2019).

29. 29.

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

30. 30.

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

31. 31.

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

32. 32.

Wang, D. et al. Evidence for Majorana bound states in an iron-based superconductor. Science 362, 333–335 (2018).

33. 33.

Zhang, P. et al. Observation of topological superconductivity on the surface of an iron-based superconductor. Science 360, 182–186 (2018).

34. 34.

Wang, Y. et al. Proximity-induced spin-triplet superconductivity and edge supercurrent in the topological Kagome metal. Preprint at https://arxiv.org/abs/2012.05898 (2020).

35. 35.

Zhao, C. C. et al. Nodal superconductivity and superconducting dome in the topological Kagome metal CsV3Sb5. Preprint at https://arxiv.org/abs/2102.08356 (2021).

36. 36.

Jiang, Y.-X. et al. Unconventional chiral charge order in kagome superconductor KV3Sb5. Nat. Mater. https://doi.org/10.1038/s41563-021-01034-y (2021).

37. 37.

Kostin, A. et al. Imaging orbital-selective quasiparticles in the Hund’s metal state of FeSe. Nat. Mater. 17, 869–874 (2018).

38. 38.

Nakayama, K. et al. Multiple energy scales and anisotropic energy gap in the charge-density-wave phase of kagome superconductor CsV3Sb5. Preprint at https://arxiv.org/abs/2104.08042 (2021).

39. 39.

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).

40. 40.

Chen, H. et al. Roton pair density wave in a strong-coupling kagome superconductor. Nature https://doi.org/10.1038/s41586-021-03983-5 (2021).

41. 41.

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. Preprint at https://arxiv.org/abs/2104.10138 (2021).

42. 42.

Fradkin, E., Kivelson, S. A. & Tranquada, J. M. Colloquium: Theory of intertwined orders in high temperature superconductors. Rev. Mod. Phys. 87, 457–482 (2015).

43. 43.

Lawler, M. J. et al. Intra-unit-cell electronic nematicity of the high-Tc copper-oxide pseudogap states. Nature 466, 347–351 (2010).

44. 44.

Kresse, G. & Hafner, J. Ab initio molecular-dynamics simulation of the liquid-metal–amorphous-semiconductor transition in germanium. Phys. Rev. B 49, 14251–14269 (1994).

45. 45.

Kresse, G. & Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 54, 11169–11186 (1996).

46. 46.

Kresse, G. & Furthmüller, J. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Comput. Mater. Sci. 6, 15–50 (1996).

47. 47.

Blöchl, P. E. Projector augmented-wave method. Phys. Rev. B 50, 17953–17979 (1994).

48. 48.

Kresse, G. & Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B 59, 1758–1775 (1999).

49. 49.

Perdew, J., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868 (1996).

50. 50.

Grimme, S., Ehrlich, S. & Goerigk, L. Effect of the damping function in dispersion corrected density functional theory. J. Comput. Chem. 32, 1456–1465 (2011).

51. 51.

Mostofi, A. A. et al. An updated version of wannier90: a tool for obtaining maximally-localised Wannier functions. Comput. Phys. Commun. 185, 2309–2310 (2014).

52. 52.

Hu, Y. et al. Charge-order-assisted topological surface states and flat bands in the kagome superconductor CsV3Sb5. Preprint at https://arxiv.org/abs/2104.12725 (2021).

## Acknowledgements

We thank K. Fujita and A. Pasupathy for valuable discussions. I.Z. gratefully acknowledges the support from the National Science Foundation grant no. NSF-DMR-1654041 and Boston College startup. S.D.W., B.R.O., L.B., S.M.L.T. and T.P. gratefully acknowledge support via the University of California Santa Barbara NSF Quantum Foundry funded via the Q-AMASE-i programme under award DMR-1906325. B.R.O. also acknowledges support from the California NanoSystems Institute through the Elings Fellowship programme. We acknowledge use of the shared computing facilities of the Center for Scientific Computing at University of California Santa Barbara, supported by NSF CNS-1725797, and the NSF Materials Research Science and Engineering Center at University of California Santa Barbara, NSF DMR-1720256. M.Y. is supported in part by the Gordon and Betty Moore Foundation through Grant GBMF8690 to UCSB. S.M.L.T. has been supported by the National Science Foundation Graduate Research Fellowship Program under grant no. DGE-1650114. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation. Z.W. acknowledges the support of US Department of Energy, Basic Energy Sciences grant no. DE-FG02-99ER45747.

## Author information

Authors

### Contributions

STM experiments and data analysis were performed by H.Z. and H.L. B.R.O. synthesized and characterized the samples under the supervision of S.D.W. S.M.L.T. performed band structure calculations. T.P., M.Y., L.B. and Z.W. provided theoretical input on the underlying physics and the interpretation of data. H.Z., S.D.W., Z.W. and I.Z. wrote the paper, with input from all authors. I.Z. supervised the project.

### Corresponding author

Correspondence to Ilija Zeljkovic.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Peer review information Nature thanks the anonymous reviewers for their contribution to the peer review of this work. Peer reviewer reports are available.

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 Cs clustering on as-cleaved Sb-terminated surface.

(a) 3D portrayal of a large-scale morphology of the Sb layer from an STM topograph. Inset is a 3D zoom-in of a small square region covering three Cs atoms. (b) As-cleaved STM topograph with several Cs atoms scattered on the surface. The apparent height of Cs atoms in (b) is approximately 2 Angstroms, and the color scale is saturated to emphasize the 4a0-CO modulation. STM setup condition: (a) Vsample = 200 mV, Iset = 10 pA; (b) Vsample = 200 mV, Iset = 50 pA. T = 4.5 K in all panels.

### Extended Data Fig. 2 Large-scale STM topograph of the Sb-terminated surface.

High resolution STM topograph over a large region encompassing the topograph from Fig. 3c. Inset shows a zoom-in on two defects that serve as main scattering sites for the wave-like QPI modulations, with different atoms superimposed on top (Cs – green, Sb – gray and V – red spheres). As it can be seen in the inset, the defects are located at the Cs site. STM setup condition: Vsample = −20 mV, Iset = 20 pA, T = 4.5 K; (inset) Vsample = 20 mV, Iset = 60 pA, T = 4.5 K.

### Extended Data Fig. 3 Quasiparticle interference imaging of the electron pocket around Γ.

(a-f) Differential conductance (dI/dV(r, V)) maps over the same region of the sample used for the analysis of the dispersion in Fig. 2, and (g-l) corresponding Fourier transforms (FTs). Green, brown and blue circles denote the atomic Bragg peaks, 2a0 charge ordering peaks q2a0-CO and unidirectional stripe charge order peaks q4a0-CO in momentum-transfer space, respectively. The red and orange arrows indicate the QPI wave vectors that we attribute to the intra-electron pocket scattering around Γ. (m) Radially-averaged FT linecut as a function of STM bias V showing the presence of q1 across Fermi energy. STM setup condition: (a) Vsample = −400 mV, Iset = 800pA, Vexc = 5 mV; (b) Vsample = −300 mV, Iset = 600 pA, Vexc = 4 mV; (c) Vsample = −200 mV, Iset = 400 pA, Vexc = 4 mV; (d) Vsample = −100 mV, Iset = 200 pA, Vexc = 4 mV; (e) Vsample = −50 mV, Iset = 100 pA, Vexc = 4 mV; (f) Vsample = 200 mV, Iset = 400 pA, Vexc = 4 mV; (m) Vsample = 10 mV, Iset = 100 pA, Vexc = 1 mV; T = 4.5 K.

### Extended Data Fig. 4 Identification of additional peaks in the Fourier transform linecut along the charge stripe direction.

Fourier transform linecut of L(r, V) maps along the q4a0-CO (charge stripe) direction at 4.5 K (same as Fig. 3g). The green dashed lines are visual guides showing the most prominent additional non-dispersive peaks. Green arrows denote all the satellite peaks we observe, approximately equally spaced from the dominant peaks. The black, blue and brown arrows indicate the dominant peaks: the low-frequency peak (qlow) likely associated with the satellite peaks, unidirectional charge order peak (q4a0-CO) and tri-directional charge order peak (q2a0-CO), respectively. STM setup condition: Vsample = 100 mV, Iset = 600pA, Vexc = 4 mV, T = 4.5 K.

### Extended Data Fig. 5 Data reproducibility across different CsV3Sb5 single crystals.

(a-c) STM topographs acquired over different CsV3Sb5 samples. (d,e) Differential conductance (dI/dV(r, V)) maps obtained on sample #1 and #3, respectively. Panels (f-j) are the corresponding Fourier transforms of the images above. STM setup condition: (a) Vsample = −20 mV, Iset = 20 pA; (b) Vsample = 300 mV, Iset = 90 pA; (c) Vsample = −40 mV, Iset = 110 pA; (d) Vsample = −4 mV, Iset = 50 pA, Vexc = 1 mV; (e) Vsample = 4 mV, Iset = 40 pA, Vexc = 1 mV.

### Extended Data Fig. 6 Bias dependence of STM topographs.

(a-d) STM topographs acquired over an identical region at 60 K under different biases. (e-h) STM topographs acquired over another region at 4.5 K under different biases. Insets in (a-h) are the associated Fourier transforms. Green, brown and blue circles denote the atomic Bragg peaks, tri-directional charge order peaks and unidirectional stripe charge order peaks in momentum-transfer space, respectively. STM setup condition: (a) Vsample = 90 mV, Iset = 30 pA; (b) Vsample = 50 mV, Iset = 30 pA; (c) Vsample = −30 mV, Iset = 40 pA; (d) Vsample = −90 mV, Iset = 40 pA; (e) Vsample = 200 mV, Iset = 400 pA; (f) Vsample = 50 mV, Iset = 100 pA; (g) Vsample = 10 mV, Iset = 20 pA; (h) Vsample = −50 mV, Iset = 100 pA.

### Extended Data Fig. 7 Density functional theory (DFT) calculation of the electronic band structure.

(a) DFT calculated band structure of CsV3Sb5 along high symmetry directions across the Brillouin zone, visualized by SUMO (Supplementary Section 1). The blue and red colors represent the contributions from Sb and V orbitals, respectively. (b) Schematic of different high-symmetry points.

### Extended Data Fig. 8 Energy dependence of the quasiparticle interference (QPI) near Fermi level.

(a-g) Two-fold symmetrized Fourier transforms (FTs) of differential conductance (dI/dV(r, V)) maps acquired over the same field-of-view on an Sb-terminated surface of sample 1. The dispersive QPI stripes are denoted by magenta (along qa) and blue (along qb,c) rectangles. At bias lower than 12 mV, the stripe features along qa are clearly visible (solid magenta rectangles), while the equivalent features along qb and qc are absent (dashed blue rectangles). The trend is reversed at a bias higher than 12 mV. Green circles denote the atomic Bragg peaks. For visual purposes, noise streaks in (c-e) along ~45 degree direction with respect to the horizontal are removed by subtracting a polynomial from each row of the raw dI/dV map before the map is rotated, FT is performed and the FT is two-fold symmetrized. (h,i) Linecuts in FTs of dI/dV(r, V) maps as a function of bias along the magenta and blue dashed lines in (d). Orange curves in (h,i) are visual guides showing the dispersion of QPI wave vectors. STM setup condition: (a) Vsample = 18 mV, Iset = 90 pA, Vexc = 1 mV; (b) Vsample = 16 mV, Iset = 200 pA, Vexc = 1 mV; (c)Vsample = 14 mV, Iset = 100 pA, Vexc = 1 mV; (d)Vsample = 12 mV, Iset = 90 pA, Vexc = 1 mV; (e)Vsample = 10 mV, Iset = 70 pA, Vexc = 1 mV; (f)Vsample = 5 mV, Iset = 60 pA, Vexc = 1 mV; (g)Vsample = −5 mV, Iset = 60 pA, Vexc = 1 mV; T = 4.5 K.

### Extended Data Fig. 9 Additional temperature-dependent STM data.

(a,b) STM topographs of an identical area of the sample at (a) 4.5 K, and (b) 50 K, and (c,d) corresponding spatially-averaged dI/dV spectra. As it can be seen from (b), the 4a0 charge ordering is nearly completely absent at this elevated temperature. The low-temperature dI/dV spectrum in (c) shows two shoulders at ±20 mV (black arrows) and gap-like features closer to Fermi energy around ± 5 to 10 mV (orange arrows). dI/dV spectrum at higher temperature in (d) (just before entering the 4a0-CO state) only shows the broad shoulders at higher energy. (e) Large-scale STM topograph and (f) Fourier transform of simultaneous dI/dV(r, V=−6 mV) map showing the presence of 4a0-CO peak and the absence of QPI (q2 and q’2 enclosed by dashed rectangles) seen at low temperature in Fig. 4 and Fig. S1. STM setup condition: (a-d) Vsample = 50 mV, Iset = 50 pA, Vexc = 1 mV; (e,f) Vsample = −8 mV, Iset = 80 pA, Vexc = 1 mV.

### Extended Data Fig. 10 Magnetization and magnetotransport measurements of CsV3Sb5 single crystals.

(a) Temperature (T) dependence of magnetization M = 4πχ (χ is magnetic susceptibility). Zero-field cooled (field cooled at 5 Oe field) magnetization is denoted by a black solid (dashed) line. (b) Angle-dependent magnetotransport measurements, plotting resistivity $$\rho$$ along the c-axis as a function of angle $$\theta$$, which is the direction of magnetic field H = 14 T applied in the ab-plane, as denoted in the inset. (c) Resistivity anisotropy as a function of temperature, calculated from the three data sets in (b) as $$\delta =\frac{2(\rho (0^\circ )+\rho (180^\circ ))}{\rho (60^\circ )+\rho (120^\circ )+\rho (240^\circ )+\rho (300^\circ )}$$.

## Supplementary information

### Supplementary Information

This file contains Supplementary Information, including Supplementary Figs. 1–6 and references.

## Rights and permissions

Reprints and Permissions

Zhao, H., Li, H., Ortiz, B.R. et al. Cascade of correlated electron states in the kagome superconductor CsV3Sb5. Nature 599, 216–221 (2021). https://doi.org/10.1038/s41586-021-03946-w

• Accepted:

• Published:

• Issue Date:

• DOI: https://doi.org/10.1038/s41586-021-03946-w

• ### Twofold van Hove singularity and origin of charge order in topological kagome superconductor CsV3Sb5

• Mingu Kang
• Shiang Fang
• Riccardo Comin

Nature Physics (2022)

• ### Charge order and superconductivity in kagome materials

• Titus Neupert
• M. Michael Denner
• M. Zahid Hasan

Nature Physics (2021)

• ### Twofold symmetry of c-axis resistivity in topological kagome superconductor CsV3Sb5 with in-plane rotating magnetic field

• Ying Xiang
• Qing Li
• Hai-Hu Wen

Nature Communications (2021)

• ### Roton pair density wave in a strong-coupling kagome superconductor

• Hui Chen
• Haitao Yang
• Hong-Jun Gao

Nature (2021)