Frieze charge stripes in a correlated kagome superconductor

Nature Physics (2026)Cite this article In kagome metals, geometric frustration, electronic correlations and band topology combine to produce a wide range of intriguing phenomena. Among them, CsCr3Sb5 offers an opportunity to investigate unconventional superconductivity in a strongly correlated kagome system, with indications of frustrated magnetism and quantum criticality. Here we demonstrate a cascade of density-wave transitions with distinct symmetries in bulk single crystals of CsCr3Sb5. Using spectroscopic imaging scanning tunnelling microscopy, we uncover a unidirectional density wave that breaks all mirror symmetries—resembling a chiral density wave—but that also retains a mirror glide symmetry. We refer to this as a frieze charge stripe order phase, as its symmetry properties correspond to one of the fundamental frieze symmetry groups. A combination of high-resolution imaging, Fourier analysis and theoretical simulations reveals the key role of sublattice degrees of freedom in stabilizing this phase, which is characterized by internal chiral textures of opposite handedness. These findings suggest that superconductivity in CsCr3Sb5 emerges from this distinct density wave state and provide fresh insights into realizing electronic phases governed by frieze symmetry groups in quantum materials.This is a preview of subscription content, access via your institution Access Nature and 54 other Nature Portfolio journals Get Nature+, our best-value online-access subscription $32.99 / 30 days cancel any timeSubscribe to this journal Receive 12 print issues and online access $259.00 per yearonly $21.58 per issueBuy this articleUSD 39.95Prices may be subject to local taxes which are calculated during checkoutData supporting the findings of this study are available via Zenodo at https://doi.org/10.5281/zenodo.18600419 (ref. 36) and upon request from the corresponding author. Source data are provided with this paper.The code that supports the findings of the study is available from the corresponding authors upon reasonable request.Fradkin, E., Kivelson, S. A. & Tranquada, J. M. Colloquium: Theory of intertwined orders in high temperature superconductors. Rev. Mod. Phys. 87, 457–482 (2015).Article ADS Google Scholar Stewart, G. R. Superconductivity in iron compounds. Rev. Mod. Phys. 83, 1589–1652 (2011).Article ADS Google Scholar Moncton, D. E., Axe, J. D. & DiSalvo, F. J. Study of superlattice formation in 2H-NbSe, and 2H-TaSe2 by neutron scattering. Phys. Rev. Lett. 34, 734–737 (1975).Article ADS Google Scholar Tranquada, J. M., Sternlieb, B. J., Axe, J. D., Nakamura, Y. & Uchida, S. Evidence for stripe correlations of spins and holes in copper oxide superconductors. Nature 375, 561–563 (1995).Article ADS Google Scholar Ishioka, J. et al. Chiral charge-density waves. Phys. Rev. Lett. 105, 176401 (2010).Article ADS Google Scholar Morier-Genoud, S. Coxeter’s frieze patterns at the crossroads of algebra, geometry and combinatorics. Bull. Lond. Math. Soc. 47, 895–938 (2015).Article MathSciNet Google Scholar Wilson, S. D. & Ortiz, B. R. AV3Sb5 kagome superconductors. Nat. Rev. Mater. 9, 420–432 (2024).Article ADS Google Scholar Neupert, T., Denner, M. M., Yin, J.-X., Thomale, R. & Hasan, M. Z. Charge order and superconductivity in kagome materials. Nat. Phys. 18, 137–143 (2021).Article Google Scholar Ortiz, B. R. et al. CsV3Sb5: a Z2 topological kagome metal with a superconducting ground state. Phys. Rev. Lett. 125, 247002 (2020).Article ADS Google Scholar Jiang, Y.-X. et al. Unconventional chiral charge order in kagome superconductor KV3Sb5. Nat. Mater. 20, 1353–1357 (2021).Article ADS Google Scholar Zhao, H. et al. Cascade of correlated electron states in the kagome superconductor CsV3Sb5. Nature 599, 216–221 (2021).Article ADS Google Scholar 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 Wu, P. et al. Unidirectional electron–phonon coupling in the nematic state of a kagome superconductor. Nat. Phys. 19, 1143–1149 (2023).Article Google Scholar Nie, L. et al. Charge-density-wave-driven electronic nematicity in a kagome superconductor. Nature 604, 59–64 (2022).Article ADS Google Scholar Xu, 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).Article Google Scholar Li, H. et al. Unidirectional coherent quasiparticles in the high-temperature rotational symmetry broken phase of AV3Sb5 kagome superconductors. Nat. Phys. 19, 637–643 (2023).

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Google Scholar Cheng, S. & Zeljkovic, I. Frieze charge-stripes in a correlated kagome superconductor CsCr3Sb5. Zenodo https://doi.org/10.5281/zenodo.18600419 (2026).Download referencesI.Z. gratefully acknowledges the support from the US Department of Energy (grant number DE-SC0025005). Z.W. and K.Z. are supported by the US Department of Energy, Basic Energy Sciences (Grant No. DE-FG02-99ER45747). G.-H.C. acknowledges the support from the National Key Research and Development Program of China (Grant Nos. 2022YFA1403202, 2023YFA1406101). Y.L. acknowledges the support from the National Science Foundation of China (Grant No. 12474132).Department of Physics, Boston College, Chestnut Hill, MA, USASiyu Cheng, Keyu Zeng, Christopher Candelora, Ziqiang Wang & Ilija ZeljkovicSchool of Physics, Key Laboratory of Quantum Precision Measurement of Zhejiang Province, Zhejiang University of Technology, Hangzhou, People’s Republic of ChinaYi LiuSchool of Physics, Institute of Fundamental and Transdisciplinary Research, Zhejiang University, Hangzhou, People’s Republic of ChinaGuang-Han CaoSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarS.C. performed STM measurements with help from C.C. Y.L. and G.-H.C. synthesized the bulk single crystals. K.Z. and S.C. performed theoretical calculations under the supervision of Z.W. and I.Z. I.Z., S.C. and Z.W. wrote the paper with the input from all the authors. I.Z. supervised the project.Correspondence to Ziqiang Wang, Guang-Han Cao or Ilija Zeljkovic.The authors declare no competing interests.Nature Physics thanks the anonymous reviewer(s) 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.(a,b) STM topographs over an identical region of the sample, acquired in back-to-back scans. We can identify the lattice structure in (a) where morphology is similar to other kagome materials in the 135 family, and superimpose it in the topograph in (b). STM setup condition: a, Vsample = -200 mV, Iset = 100 pA; b, Vsample = 200 mV, Iset = 100 pA.Source dataFourier transform linecuts, offset for clarity, along the Q1 direction, acquired over a different area of the sample with a different microscopic tip compared to data in Fig. 2. STM setup conditions: Iset = 300 pA.(a,b) STM topograph and corresponding Fourier transform obtained on sample 1, also from main text. (c,d) STM topograph and corresponding Fourier transform obtained on sample 2. Data on the two samples was obtained using two different STM tip wires. STM setup conditions: a, Vsample = -500 mV, Iset = 200 pA; b, Vsample = 300 mV, Iset = 200 pA.(a,b) STM topographs (left) and zoomed-in regions (right). Dashed green and white lines denote mirror symmetries that are broken. Topograph in (a) was taken on sample 1 using tip wire 1, and (b) is acquired on a different sample with a different STM tip. STM setup conditions: a, Vsample = 200 mV, Iset = 100 pA; b, Vsample = 100 mV, Iset = 200 pA.(a) STM topograph (lower half) and its mirror image along the x-axis (upper half). It can be seen that the arrow-like pattern has an abrupt transition between the two images when viewed from up to down (see for example the white dashed circles and the yellow dashed line). (b) The same two topographs from (a) but with the mirror image (upper one) offset horizontally by \(\cos \frac{\pi }{6}\) of the lattice constant a0. It can be seen that now the arrow-like pattern is aligned up between the original image and the transformed image. c Same as (b) but for a different STM bias. STM setup conditions: a-c, Iset = 100 pA.Source data(a) Large STM topograph showing multiple domains. (b,c) Smaller zoom-ins on the two regions enclosed by dashed red and green rectangles, and (d,e) associated Fourier transforms. Both regions show the absence of Q2 but strong Bragg satellite peaks. STM setup condition: (a) Vsample = 50 mV, Iset = 300 pA.We work with the same model for the Q2 density wave from the main text: \({\Delta }_{\mathrm{CDW}}({{\bf{r}}}_{i})={\sum }_{n,\alpha }{\rho }_{n,\alpha }\cos (n[{{\bf{Q}}}_{2}+{{\bf{Q}}}_{Bragg}^{\alpha }]\cdot {{\bf{r}}}_{i}+\theta )\). (a) Simulated topograph with a simple modulation \({\Delta }_{{\rm{CDW}}}({{\bf{r}}}_{i})=\cos ({{\bf{Q}}}_{2}\cdot {{\bf{r}}}_{i})\), where \({{\bf{Q}}}_{Bragg}^{\alpha }\) is not introduced as there is no sublattice phase difference. The Q2 peak appears around the FT center, and the modulation is unidirectional. The mirror symmetries along the y-axis and along the x-axis remain intact. (b) Simulated topograph for n=1 and θ=0, as the expression becomes \({\Delta }_{\mathrm{CDW}}({{\bf{r}}}_{i})={\sum }_{\alpha =a,b}{\rho }_{\alpha }\)\(\cos ([{{\bf{Q}}}_{2}+{{\bf{Q}}}_{Bragg}^{\alpha }]\cdot {{\bf{r}}}_{i})={\sum }_{\alpha =a,b}{\rho }_{\alpha }\cos ({{\bf{Q}}}_{2}\cdot {{\bf{r}}}_{i}+{\phi }_{\alpha })\). The term \({\phi }_{\alpha }={{\bf{Q}}}_{Bragg}^{\alpha }\cdot {{\bf{r}}}_{i}\) brings different phases to the four sublattices, in the order of Sb, Cr1, Cr2, Cr3. For α = a, ϕa = 0, π, π, 0, for α = b, ϕb = 0, 0, π, π. The inset in (b) only shows the modulation for α = a. Importantly, the different phases ϕα within each sublattices result in a complete annihilation of the Q2 peaks around the FT center. For α = c, the mirror symmetries along the y-axis remain because \({{\bf{Q}}}_{Bragg}^{c}\) is perpendicular to Q2. If α = a or α = b, the density wave will break the mirror symmetries along the y-axis. If these mirror planes mismatch with the mirror planes of the kagome lattice by a phase shift θ, then all mirror symmetries are broken. There are also inversion symmetries at the nodes of the wave, which can be preserved by overlapping with kagome inversion centers at the sites, for example when θ = π/8. (c,d) Fourier transforms of (a,b), respectively.(a,b) A second data sequence showing Fourier transforms (FTs) of topographs of the same area at different temperatures. The insets in both panels are FT linecuts taken along the dashed blue line. In our experiment, 48 K is measured first, and then 50 K. It can be seen that Q1 again vanishes at 50 K, but is clearly present at 48 K, consistent with the dataset in the main paper. (c,d) The same Fourier transform as that used in Fig. 2d acquired in forwards direction, and equivalent image acquired in the backwards direction. The consistency between the two further excludes the possibility of Q1 being an artifact or noise. The dashed red circle area has an average background intensity of 3.6 × 10−4, with standard deviation of 2.3 × 10−4. The Q1 peak has the intensity of 1.5 × 10−3, which stands out about 5 standard deviations from the background. STM setup condition: (a,b)Vsample = -500 mV, Iset = 50 pA.(a) Resistivity as function of temperature upon cooling (blue) and warming up (red) showing a thermal hysteresis and an inflection point around 45 K. (b) Difference between the two curves in (a) showing a peak at 44 K. (c) Derivative of resistivity with respect to temperature, showing an inflection point seen by eye in (a).Source data(a,b) STM topograph (a) and the corresponding dI/dV map (b), measured on the Sb surface. (c) Waterfall plot of dI/dV spectra taken along the orange line in (a). It can be seen that the spectral weight is modulated by the density wave. (d) Average dI/dV spectrum measured on the Sb surface, showing a partial gap roughly centered at the Fermi level of about 20 meV width. STM setup condition: a,b,c, Vsample = 100 mV, Iset = 200 pA, Vlockin = 1 mV; d, Vsample = 100 mV, Iset = 300 pA, Vlockin = 2 mV; Lockin frequency was 913 Hz.Source data.Source data.Source data.Source data.Source data.Source data.Springer Nature or its licensor (e.g. a society or other partner) 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 permissionsCheng, S., Zeng, K., Liu, Y. et al. Frieze charge stripes in a correlated kagome superconductor. Nat. Phys. (2026). https://doi.org/10.1038/s41567-026-03232-4Download citationReceived: 10 June 2025Accepted: 25 February 2026Published: 02 April 2026Version of record: 02 April 2026DOI: https://doi.org/10.1038/s41567-026-03232-4Anyone you share the following link with will be able to read this content:Sorry, a shareable link is not currently available for this article. Provided by the Springer Nature SharedIt content-sharing initiative