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V51 NMR evidence for interlayer-modulated charge order and a first-order low-temperature transition in CsV3Sb5

Xiaoling Wang1,*, Arneil P. Reyes2, Hrishit Banerjee3, Andrea N. Capa Salinas4, Stephen Wilson4, and Brenden R. Ortiz5

  • *Contact author: xiaoling.wang@csueastbay.edu
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Phys. Rev. B 112, 235123 – Published 8 December, 2025

DOI: https://doi.org/10.1103/91c9-z267

Abstract

Charge order in the kagome superconductor CsV3Sb5 exhibits a complex three-dimensional organization and intermediate-temperature anomalies whose bulk character has remained unsettled. We use orientation-dependent V51 NMR as a site-selective probe to determine the stacking of the charge density wave (CDW) state and its thermal evolution. Below TCDW≈94K, the field-linear splitting of the V51 central transition together with the anisotropy of the Knight shift tensor identify an interlayer-modulated 3q CDW whose local environments are consistent with a four-layer 2×2×4 stacking with mixed trihexagonal/Star-of-David distortions, in agreement with synchrotron x-ray determinations. For comparison, RbV3Sb5 serves as a reference exhibiting a uniform trihexagonal 2×2×2 stacking, allowing us to isolate features unique to the 2×2×4 state in CsV3Sb5. With H0∥c, the V51 quadrupolar satellites through the intermediate temperature scale near TCO≈65K reorganize into two well-resolved electric-field-gradient manifolds that coexist over a finite interval; their relative spectral weights interchange on cooling while the total integrated satellite intensity remains conserved and νQ within each manifold is nearly temperature independent. The coexistence without critical broadening, together with conserved intensity, provides bulk evidence consistent with a first-order charge-order transition near TCO. Our measurements do not resolve whether this lower-temperature transition corresponds to a distinct in-plane order or a reorganization of the 3q state; rather, they delimit this window and provide bulk, site-resolved constraints that connect prior reported anomalies to a thermodynamic first-order transition.

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References (50)

  1. Brenden R. Ortiz, Lidia C. Gomes, Jennifer R. Morey, M. Winiarski, M. Bordelon, John S. Mangum, Iain W. H. Oswald, J. A. Rodriguez-Rivera, James R. Neilson, Stephen D. Wilson, E. Ertekin, T. M. McQueen, and Eric S. Toberer, New kagome prototype materials: Discovery of KV3Sb5, RbV3Sb5, and CsV3Sb5, Phys. Rev. Mater. 3, 094407 (2019).
  2. Brenden R. Ortiz, Samuel M. L. Teicher, Y. Hu, Julia L. Zuo, Paul M. Sarte, Emily C. Schueller, A. M. Milinda Abeykoon, Mathew J. Krogstad, S. Rosenkranz, R. Osborn, R. Seshadri, L. Balents, J. He, and Stephen D. Wilson, CsV3Sb5:A ℤ2 topological kagome metal with a superconducting ground state, Phys. Rev. Lett. 125, 247002 (2020).
  3. Q. Yin, Z. Tu, C. Gong, Y. Fu, S. Yan, and H. Lei, Superconductivity and normal-state properties of kagome metal RbV3Sb5 single crystals, Chin. Phys. Lett. 38, 037403 (2021).
  4. H. Tan, Y. Liu, Z. Wang, and B. Yan, Charge density waves and electronic properties of superconducting kagome metals, Phys. Rev. Lett. 127, 046401 (2021).
  5. M. Kang, S. Fang, L. Ye, H. C. Po, J. Denlinger, C. Jozwiak, A. Bostwick, E. Rotenberg, E. Kaxiras, J. G. Checkelsky, and R. Comin, Twofold van hove singularity and origin of charge order in topological kagome superconductor CsV3Sb5, Nat. Phys. 18, 301 (2022).
  6. Y. Hu, S. M. L. Teicher, B. R. Ortiz, Y. Luo, S. Peng, L. Huai, J. Ma, N. C. Plumb, S. D. Wilson, J. He, and M. Shi, Rich nature of van hove singularities in kagome superconductor CsV3Sb5, Nat. Commun. 13, 2220 (2022).
  7. Morten H. Christensen, T. Birol, Brian M. Andersen, and Rafael M. Fernandes, Theory of the charge density wave in AV3Sb5 kagome metals, Phys. Rev. B 104, 214513 (2021).
  8. H. LaBollita and Antia S. Botana, Tuning the van Hove singularities in AV3Sb5(A=K,Rb,Cs) via pressure and doping, Phys. Rev. B 104, 205129 (2021).
  9. H. Li, T. T. Zhang, T. Yilmaz, Y. Y. Pai, C. E. Marvinney, A. Said, Q. W. Yin, C. S. Gong, Z. J. Tu, E. Vescovo, C. S. Nelson, R. G. Moore, S. Murakami, H. C. Lei, H. N. Lee, B. J. Lawrie, and H. Miao, Observation of unconventional charge density wave without acoustic-phonon anomaly in kagome superconductors AV3Sb5(A=Rb,Cs), Phys. Rev. X 11, 031050 (2021).
  10. Z. Liang, X. Hou, F. Zhang, W. Ma, P. Wu, Z. Zhang, F. Yu, J. J. Ying, K. Jiang, L. Shan, Z. Wang, and X.-H. Chen, Three-dimensional charge density wave and surface-dependent vortex-core states in a kagome superconductor CsV3Sb5, Phys. Rev. X 11, 031026 (2021).
  11. Brenden R. Ortiz, Samuel M. L. Teicher, L. Kautzsch, Paul M. Sarte, N. Ratcliff, J. Harter, Jacob P. C. Ruff, R. Seshadri, and Stephen D. Wilson, Fermi surface mapping and the nature of charge-density-wave order in the kagome superconductor CsV3Sb5, Phys. Rev. X 11, 041030 (2021).
  12. M. Kang, S. Fang, L. Ye, J. S. You, S. Fang, A. Levitan, M. Han, C. Jozwiak, A. Bostwick, E. Rotenberg, E. Kaxiras, J. G. Checkelsky, and R. Comin, Charge order landscape and competition with superconductivity in kagome metals, Nat. Mater. 22, 186 (2023).
  13. H. Zhao, H. Li, B. R. Ortiz, S. D. Wilson, and M. Z. Hasan, Cascade of correlated electron states in a kagome superconductor CsV3Sb5, Nature (London) 599, 216 (2021).
  14. L. Kautzsch, Brenden R. Ortiz, K. Mallayya, J. Plumb, G. Pokharel, Jacob P. C. Ruff, Z. Islam, Eun A. Kim, R. Seshadri, and Stephen D. Wilson, Structural evolution of the kagome superconductors AV3Sb5 (A = K, Rb, and Cs) through charge-density-wave order, Phys. Rev. Mater. 7, 024806 (2023).
  15. G. Liu, X. Ma, K. He, Q. Li, H. Tan, Y. Liu, J. Xu, W. Tang, K. Watanabe, T. Taniguchi, L. Gao, Y. Dai, H.-H. Wen, B. Yan, and X. Xi, Observation of anomalous amplitude modes in the kagome metal CsV3Sb5, Nat. Commun. 13, 3461 (2022).
  16. N. Ratcliff, L. Hallett, Brenden R. Ortiz, Stephen D. Wilson, and John W. Harter, Coherent phonon spectroscopy and interlayer modulation of charge density wave order in the kagome metal CsV3Sb5, Phys. Rev. Mater. 5, L111801 (2021).
  17. C. Mu, Q. Yin, Z. Tu, C. Gong, H. Lei, Z. Li, and J. Luo, S-wave superconductivity in kagome metal CsV3Sb5 revealed by Sb121/123 NQR and V51 NMR measurements, Chin. Phys. Lett. 38, 077402 (2021).
  18. D.-W. Song, L.-X. Zheng, F.-H. Yu, J. Li, L.-P. Nie, M. Shan, D. Zhao, S.-J. Li, B.-L. Kang, Z.-M. Wu, Y.-B. Zhou, K.-L. Sun, K. Liu, X.-G. Luo, Z.-Y. Wang, J.-J. Ying, X.-G. Wan, T. Wu, and X.-H. Chen, Orbital ordering and fluctuations in a kagome superconductor CsV3Sb5, Sci. China: Phys. Mech. Astron. 65, 247462 (2022).
  19. J. Luo, N. W. Wang, D. X. Zhang, L. M. Zhang, Z. Y. Wang, H. Y. Ma, R. Zhang, S. J. Tian, Y. F. Zhang, H. C. Lei, J. Q. Yan, D. G. Mandrus, and Y. H. Zhang, Possible star-of-david pattern charge density wave with additional modulation in the kagome superconductor CsV3Sb5, npj Quantum Mater. 7, 30 (2022).
  20. L. Zheng, Z. Wu, Y. Yang, L. Nie, M. Shan, K. Sun, D. Song, F. Yu, J. Li, D. Zhao, S. Li, B. Kang, Y. Zhou, K. Liu, Z. Xiang, J. Ying, Z. Wang, T. Wu, and X. Chen, Emergent charge order in pressurized kagome superconductor CsV3Sb5, Nature (London) 611, 682 (2022).
  21. X. Y. Feng, Z. Zhao, J. Luo, J. Yang, A. F. Fang, H. T. Yang, H. J. Gao, R. Zhou, and G.-q. Zheng, Commensurate-to-incommensurate transition of charge-density-wave order and a possible quantum critical point in pressurized kagome metal CsV3Sb5, npj Quantum Mater. 8, 23 (2023).
  22. J. Frassineti, P. Bonfà, G. Allodi, E. Garcia, R. Cong, Brenden R. Ortiz, Stephen D. Wilson, R. De Renzi, Vesna F. Mitrović, and S. Sanna, Microscopic nature of the charge-density wave in the kagome superconductor RbV3Sb5, Phys. Rev. Res. 5, L012017 (2023).
  23. X. Zhang, Y. Li, J. Zheng, F. Zhou, Q. Wu, X. Xi, Y. Lau, Z. Wang, and W. Wang, NMR study of charge density wave phase in the kagome metal RbV3Sb5, Appl. Phys. Lett. 124, 093106 (2024).
  24. X. Y. Feng, Z. Zhao, J. Luo, Y. Z. Zhou, J. Yang, A. F. Fang, H.-T. Yang, H.-J. Gao, R. Zhou, and G.-q. Zheng, Fully-gapped superconductivity with rotational symmetry breaking in pressurized kagome metal CsV3Sb5, Nat. Commun. 16, 3643 (2025).
  25. Yuzki M. Oey, Brenden R. Ortiz, F. Kaboudvand, J. Frassineti, E. Garcia, R. Cong, S. Sanna, Vesna F. Mitrović, R. Seshadri, and Stephen D. Wilson, Fermi level tuning and double-dome superconductivity in the kagome metal CsV3Sb5−xSnx, Phys. Rev. Mater. 6, L041801 (2022).
  26. A. N. Capa Salinas, B. R. Ortiz, C. Bales, J. Frassineti, V. F. Mitrović, and S. D. Wilson, Electron–hole asymmetry in the phase diagram of carrier-tuned CsV3Sb5, Front. Electron. Mater. 3, 1257490 (2023).
  27. See Supplemental Material at http://link.aps.org/supplemental/10.1103/91c9-z267 for experimental details of V51 NMR and DFT calculations with additional band-structure data.
  28. P. E. Blöchl, Projector augmented-wave method, Phys. Rev. B 50, 17953 (1994).
  29. G. Kresse and J. Hafner, Ab initio molecular dynamics for liquid metals, Phys. Rev. B 47, 558 (1993).
  30. G. Kresse and J. Furthmüller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Phys. Rev. B 54, 11169 (1996).
  31. John P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996).
  32. M. Wenzel, B. R. Ortiz, S. D. Wilson, M. Dressel, A. A. Tsirlin, and E. Uykur, Optical study of RbV3Sb5: Multiple density-wave gaps and phonon anomalies, Phys. Rev. B 105, 245123 (2022).
  33. Q. Stahl, D. Chen, T. Ritschel, C. Shekhar, E. Sadrollahi, M. C. Rahn, O. Ivashko, M. v. Zimmermann, C. Felser, and J. Geck, Temperature-driven reorganization of electronic order in CsV3Sb5, Phys. Rev. B 105, 195136 (2022).
  34. Q. Xiao, Y. Lin, Q. Li, X. Zheng, S. Francoual, C. Plueckthun, W. Xia, Q. Qiu, S. Zhang, Y. Guo, J. Feng, and Y. Peng, Coexistence of multiple stacking charge density waves in kagome superconductor CsV3Sb5, Phys. Rev. Res. 5, L012032 (2023).
  35. Y.-X. Jiang, J.-X. Yin, M. M. Denner, N. Shumiya, B. R. Ortiz, G. Xu, Z. Guguchia, J. He, M. S. Hossain, X. Liu et al., Unconventional chiral charge order in kagome superconductor KV3Sb5, Nat. Mater. 20, 1353 (2021).
  36. T. Kato, Y. Li, T. Kawakami, M. Liu, K. Nakayama, Z. Wang, A. Moriya, K. Tanaka, T. Takahashi, Y. Yao, and T. Sato, Three-dimensional energy gap and origin of charge-density wave in kagome superconductor KV3Sb5, Commun. Mater. 3, 30 (2022).
  37. K. Nakayama, Y. Li, T. Kato, M. Liu, Z. Wang, T. Takahashi, Y. Yao, and T. Sato, Multiple energy scales and anisotropic energy gap in the charge-density-wave phase of the kagome superconductor CsV3Sb5, Phys. Rev. B 104, L161112 (2021).
  38. M. Y. Jeong, Hyeok-J. Yang, H. S. Kim, Y. B. Kim, S. B. Lee, and M. J. Han, Crucial role of out-of-plane sb p orbitals in van hove singularity formation and electronic correlations in the superconducting kagome metal CsV3Sb5, Phys. Rev. B 105, 235145 (2022).
  39. Ethan T. Ritz, Rafael M. Fernandes, and T. Birol, Impact of sb degrees of freedom on the charge density wave phase diagram of the kagome metal CsV3Sb5, Phys. Rev. B 107, 205131 (2023).
  40. H. Li, X. Liu, Y. B. Kim, and Hae-Y. Kee, Origin of π-shifted three-dimensional charge density waves in the kagome metal AV3Sb5 (A = K, Rb, and Cs), Phys. Rev. B 108, 075102 (2023).
  41. P. P. Man, Second-order quadrupole effects on Hahn echoes in fast-rotating solids at the magic angle, Phys. Rev. B 55, 8406 (1997).
  42. R. D. Walker and B. C. Gerstein, Second-order quadrupolar echo, Phys. Rev. B 31, 3167 (1985).
  43. T. Imai, S. K. Takahashi, A. Arsenault, A. W. Acton, D. Lee, W. He, Y. S. Lee, and M. Fujita, Revisiting Cu63 NMR evidence for charge order in superconducting La1.885Sr0.115CuO4, Phys. Rev. B 96, 224508 (2017).
  44. L. A. O'Dell, K. J. Harris, and R. W. Schurko, Optimized excitation pulses for the acquisition of static NMR powder patterns from half-integer quadrupolar nuclei, J. Magn. Reson. 203, 156 (2010).
  45. H.-T. Kwak, J. Tang, P. R. Vasconcelos, D. K. Lee, D. P. Weitekamp, C. J. Pike, D. P. Weliky, G. S. Boutis, and T. M. J. Grandinetti, Selective suppression and excitation of solid-state NMR resonances based on quadrupole coupling constants, J. Magn. Reson. 160, 107 (2003).
  46. S. Wu, Brenden R. Ortiz, H. Tan, Stephen D. Wilson, B. Yan, T. Birol, and G. Blumberg, Charge density wave order in the kagome metal AV3Sb5 (A = Cs, Rb, K), Phys. Rev. B 105, 155106 (2022).
  47. D. Wulferding, S. Lee, Y. Choi, Q. Yin, Z. Tu, C. Gong, H. Lei, S. Yousuf, J. Song, H. Lee, T. Park, and Kwang-Y. Choi, Emergent nematicity and intrinsic versus Extrinsic electronic scattering processes in the kagome metal CsV3Sb5, Phys. Rev. Res. 4, 023215 (2022).
  48. L. Nie et al., Charge-density-wave-driven electronic nematicity in a kagome superconductor, Nature (London) 604, 59 (2022).
  49. S. Han, C. S. Tang, L. Li, Y. Liu, H. Liu, J. Gou, J. Wu, D. Zhou, P. Yang, C. Diao et al., Orbital-hybridization-driven charge density wave transition in CsV3Sb5 kagome superconductor, Adv. Mater. 35, 2209010 (2023).
  50. H. Li, G. Fabbris, A. H. Said, Y. Pai, Q. Yin, C. Gong, Z. Tu, H. Lei, P. Sun, S. D. Wilson, B. Yan, R. Thomale, and H. Miao, Discovery of Conjoined charge density waves in the kagome superconductor CsV3Sb5, Nat. Commun. 13, 6348 (2022).

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Phys. Rev. B 112, 235123– Published 8 December, 2025
  • Received 4 September 2025
  • Revised 31 October 2025
  • Accepted 12 November 2025
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