- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Letter
  • Open Access

Microscopic nature of the charge-density wave in the kagome superconductor RbV3Sb5

Jonathan Frassineti1, Pietro Bonfà2,*, Giuseppe Allodi2, Erick Garcia3, Rong Cong3, Brenden R. Ortiz4, Stephen D. Wilson4, Roberto De Renzi2, Vesna F. Mitrović3,† et al.

Samuele Sanna1

  • 1Department of Physics and Astronomy “A. Righi”, University of Bologna and INFN Sezione di Bologna, via Berti Pichat 6/2, 40127 Bologna, Italy
  • 2Department of Mathematical, Physical and Computer Sciences, University of Parma, Parco Area delle Scienze 7/A, 43124 Parma, Italy
  • 3Department of Physics, Brown University, Providence, Rhode Island 02912, USA
  • 4Materials Department and California Nanosystems Institute, University of California Santa Barbara, Santa Barbara, California 93106, USA

  • *pietro.bonfa@unipr.it
  • †vesna_mitrovic@brown.edu
PDF

Phys. Rev. Research 5, L012017 – Published 10 February, 2023

DOI: https://doi.org/10.1103/PhysRevResearch.5.L012017

Abstract

The recently discovered vanadium-based Kagome metals AV3Sb5 (A = K, Rb, Cs) undergo a unique phase transition into charge-density wave (CDW) order which precedes both unconventional superconductivity and time-reversal symmetry breaking. Therefore the essential first step in building a full understanding of the role of CDW in establishing these unconventional phases is to unveil the symmetries and the microscopic nature of the charge-ordered phase. Here, we determine the exact structure of the 2×2×2 superlattice that develops below the charge-density wave ordering temperature (TCDW) in RbV3Sb5. We present a comprehensive set of V51, Rb87, and Sb121 nuclear magnetic resonance (NMR) measurements and density functional theory simulations of NMR observables to provide a unique site-selective view into the local nature of the charge-ordered phase. The combination of these experimental results with simulations provides compelling evidence that the CDW structure prevailing below 103 K in RbV3Sb5 is the so-called inverse Star of David pattern, π-shifted along the c axis. These findings put severe constraints on the topology of these Kagome compounds and thus provide essential guidance for the development of an appropriate theoretical framework for predicting properties of exotic electronic orders arising within the CDW phase.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (60)

  1. S. Depenbrock, I. P. McCulloch, and U. Schollwöck, Nature of the Spin-Liquid Ground State of the S=1/2 Heisenberg Model on the Kagome Lattice, Phys. Rev. Lett. 109, 067201 (2012).
  2. N. Ghimire and I. Mazin, Topology and correlations on the kagome lattice, Nat. Mater. 19, 137 (2020).
  3. D. A. Huse and A. D. Rutenberg, Classical antiferromagnets on the Kagome lattice, Phys. Rev. B 45, 7536 (1992).
  4. A. Kitaev, Anyons in an exactly solved model and beyond, Ann. Phys. 321, 2 (2006).
  5. W. Koshibae and S. Maekawa, Electronic State of a CoO2 Layer with Hexagonal Structure: A Kagome Lattice Structure in a Triangular Lattice, Phys. Rev. Lett. 91, 257003 (2003).
  6. Z. Li, J. Zhuang, L. Wang, H. Feng, Q. Gao, X. Xu, W. Hao, X. Wang, C. Zhang, K. Wu, S. X. Dou, L. Chen, Z. Hu, and Y. Du, Realization of flat band with possible nontrivial topology in electronic Kagome lattice, Sci. Adv. 4, eaau4511 (2018).
  7. K. Morita, M. Kishimoto, and T. Tohyama, Ground-state phase diagram of the Kitaev-Heisenberg model on a kagome lattice, Phys. Rev. B 98, 134437 (2018).
  8. R. R. P. Singh and D. A. Huse, Triplet and singlet excitations in the valence bond crystal phase of the kagome lattice Heisenberg model, Phys. Rev. B 77, 144415 (2008).
  9. M. Taillefumier, J. Robert, C. L. Henley, R. Moessner, and B. Canals, Semiclassical spin dynamics of the antiferromagnetic Heisenberg model on the kagome lattice, Phys. Rev. B 90, 064419 (2014).
  10. M. G. Yamada, T. Soejima, N. Tsuji, D. Hirai, M. Dincă, and H. Aoki, First-principles design of a half-filled flat band of the kagome lattice in two-dimensional metal-organic frameworks, Phys. Rev. B 94, 081102(R) (2016).
  11. M. L. Kiesel, C. Platt, and R. Thomale, Unconventional Fermi Surface Instabilities in the Kagome Hubbard Model, Phys. Rev. Lett. 110, 126405 (2013).
  12. W.-S. Wang, Z.-Z. Li, Y.-Y. Xiang, and Q.-H. Wang, Competing electronic orders on kagome lattices at van Hove filling, Phys. Rev. B 87, 115135 (2013).
  13. S.-L. Yu and J.-X. Li, Chiral superconducting phase and chiral spin-density-wave phase in a Hubbard model on the kagome lattice, Phys. Rev. B 85, 144402 (2012).
  14. Y. Wang, S. Yang, P. K. Sivakumar, B. R. Ortiz, S. M. L. Teicher, H. Wu, A. K. Srivastava, C. Garg, D. Liu, S. S. P. Parkin, E. S. Toberer, T. McQueen, S. D. Wilson, and M. N. Ali, Proximity-induced spin-triplet superconductivity and edge supercurrent in the topological Kagome metal, K1−xV3Sb5, arXiv:2012.05898.
  15. B. R. Ortiz, L. C. Gomes, J. R. Morey, M. Winiarski, M. Bordelon, J. S. Mangum, I. W. H. Oswald, J. A. Rodriguez-Rivera, J. R. Neilson, S. D. Wilson, E. Ertekin, T. M. McQueen, and E. S. Toberer, New kagome prototype materials: Discovery of KV3Sb5,RbV3Sb5, and CsV3Sb5, Phys. Rev. Mater. 3, 094407 (2019).
  16. B. R. Ortiz, S. M. L. Teicher, Y. Hu, J. L. Zuo, P. M. Sarte, E. C. Schueller, A. M. M. Abeykoon, M. J. Krogstad, S. Rosenkranz, R. Osborn, R. Seshadri, L. Balents, J. He, and S. D. Wilson, CsV3Sb5: A Z2 Topological Kagome Metal with a Superconducting Ground State, Phys. Rev. Lett. 125, 247002 (2020).
  17. S.-Y. Yang, Y. Wang, B. R. Ortiz, D. Liu, J. Gayles, E. Derunova, R. Gonzalez-Hernandez, L. Šmejkal, Y. Chen, S. S. P. Parkin, S. D. Wilson, E. S. Toberer, T. McQueen, and M. N. Ali, Giant, unconventional anomalous Hall effect in the metallic frustrated magnet candidate, KV3Sb5, Sci. Adv. 6, eabb6003 (2020).
  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. N. Shumiya, M. S. Hossain, J.-X. Yin, Y.-X. Jiang, B. R. Ortiz, H. Liu, Y. Shi, Q. Yin, H. Lei, S. S. Zhang, G. Chang, Q. Zhang, T. A. Cochran, D. Multer, M. Litskevich, Z.-J. Cheng, X. P. Yang, Z. Guguchia, S. D. Wilson, and M. Z. Hasan, Intrinsic nature of chiral charge order in the kagome superconductor RbV3Sb5, Phys. Rev. B 104, 035131 (2021).
  20. Y. Jiang et al., Unconventional chiral charge order in kagome superconductor KV3Sb5, Nat. Mater. 20, 1353 (2021).
  21. Y. M. Oey, B. R. Ortiz, F. Kaboudvand, J. Frassineti, E. Garcia, R. Cong, S. Sanna, V. F. Mitrovic, R. Seshadri, and S. D. Wilson, Fermi level tuning and double-dome superconductivity in the kagome metal CsV3Sb5−xSnx, Phys. Rev. Mater. 6, L041801 (2022).
  22. C. Mielke III, D. Das, J.-X. Yin, H. Liu, R. Gupta, Y.-X. Jiang, M. Medarde, X. Wu, H. C. Lei, J. Chang, P. Dai, Q. Si, H. Miao, R. Thomale, T. Neupert, Y. Shi, R. Khasanov, M. Z. Hasan, H. Luetkens, and Z. Guguchia, Time-reversal symmetry-breaking charge order in a kagome superconductor, Nature 602, 245 (2022).
  23. E. M. Kenney, B. R. Ortiz, C. Wang, S. D. Wilson, and M. J. Graf, Absence of local moments in the kagome metal KV3Sb5 as determined by muon spin spectroscopy, J. Phys.: Condens. Matter 33, 235801 (2021).
  24. M. Kang, S. Fang, J. Yoo, B. R. Ortiz, Y. Oey, J. Choi, S. H. Ryu, J. Kim, C. Jozwiak, A. Bostwick, E. Rotenberg, E. Kaxiras, J. Checkelsky, S. D. Wilson, J.-H. Park, and R. Comin, Charge order landscape and competition with superconductivity in kagome metals, Nature Materials 22, 186 (2023).
  25. Y. Hu, X. Wu, B. R. Ortiz, S. Ju, X. Han, J. Ma, N. C. Plumb, M. Radovic, R. Thomale, S. D. Wilson, A. P. Schnyder, and M. Shi, Rich nature of Van Hove singularities in Kagome superconductor CsV3Sb5, Nat. Commun. 13, 2220 (2022).
  26. A. Consiglio, T. Schwemmer, X. Wu, W. Hanke, T. Neupert, R. Thomale, G. Sangiovanni, and D. Di Sante, Van hove tuning of AV3Sb5 kagome metals under pressure and strain, Phys. Rev. B 105, 165146 (2022).
  27. M. Y. Jeong, H.-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).
  28. J. Wilson, F. D. Salvo, and S. Mahajan, Charge-density waves and superlattices in the metallic layered transition metal dichalcogenides, Adv. Phys. 24, 117 (1975).
  29. K. Rossnagel, On the origin of charge-density waves in select layered transition-metal dichalcogenides, J. Phys.: Condens. Matter 23, 213001 (2011).
  30. M. H. Christensen, T. Birol, B. M. Andersen, and R. M. Fernandes, Loop currents in AV3Sb5 kagome metals: Multipolar and toroidal magnetic orders, Phys. Rev. B 106, 144504 (2022).
  31. L. Nie, K. Sun, W. Ma, D. Song, L. Zheng, Z. Liang, P. Wu, F. Yu, J. Li, M. Shan, D. Zhao, S. Li, B. Kang, Z. Wu, Y. Zhou, K. Liu, Z. Xiang, J. Ying, Z. Wang, T. Wu et al., Charge-density-wave-driven electronic nematicity in a kagome superconductor, Nature 604, 59 (2022).
  32. C. Mu, Q. Yin, Z. Tu, C. Gong, P. Zheng, H. Lei, Z. Li, and J. Luo, Tri-hexagonal charge order in kagome metal CsV3Sb5 revealed by Sb121 nuclear quadrupole resonance, Chin. Phys. B 31, 017105 (2022).
  33. 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).
  34. A. Ptok, A. Kobiałka, M. Sternik, J. Łażewski, P. T. Jochym, A. M. Oleś, and P. Piekarz, Dynamical study of the origin of the charge density wave in AV3Sb5 (A=K, Rb, Cs) compounds, Phys. Rev. B 105, 235134 (2022).
  35. 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).
  36. 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).
  37. Z. Jiang, H. Ma, W. Xia, Q. Xiao, Z. Liu, Z. Liu, Y. Yang, J. Ding, Z. Huang, J. Liu, Y. Qiao, J. Liu, Y. Peng, S. Cho, Y. Guo, J. Liu, and D. Shen, Observation of electronic nematicity driven by three-dimensional charge density wave in kagome lattice KV3Sb5, arXiv:2208.01499.
  38. 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).
  39. J. Luo, Z. Zhao, Y. Z. Zhou, J. Yang, A. F. Fang, H. T. Yang, H. J. Gao, R. Zhou, and G.-q. Zheng, Possible Star-of-David pattern charge density wave with additional modulation in the kagome superconductor CsV3Sb5, npj Quantum Mater. 7, 30 (2022).
  40. B. R. Ortiz, S. M. L. Teicher, L. Kautzsch, P. M. Sarte, N. Ratcliff, J. Harter, J. P. C. Ruff, R. Seshadri, and S. D. Wilson, Fermi Surface Mapping and the Nature of Charge-Density-Wave Order in the Kagome Superconductor CsV3Sb5, Phys. Rev. X 11, 041030 (2021).
  41. Y. Hu, X. Wu, B. R. Ortiz, X. Han, N. C. Plumb, S. D. Wilson, A. P. Schnyder, and M. Shi, Coexistence of trihexagonal and star-of-David pattern in the charge density wave of the kagome superconductor AV3Sb5, Phys. Rev. B 106, L241106 (2022).
  42. H. Luo, Q. Gao, H. Liu, Y. Gu, D. Wu, C. Yi, J. Jia, S. Wu, X. Luo, Y. Xu, L. Zhao, Q. Wang, H. Mao, G. Liu, Z. Zhu, Y. Shi, K. Jiang, J. Hu, Z. Xu, and X. J. Zhou, Electronic nature of charge density wave and electron-phonon coupling in kagome superconductor KV3Sb5, Nat. Commun. 13, 273 (2022).
  43. 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).
  44. S. Cho, H. Ma, W. Xia, Y. Yang, Z. Liu, Z. Huang, Z. Jiang, X. Lu, J. Liu, Z. Liu, J. Li, J. Wang, Y. Liu, J. Jia, Y. Guo, J. Liu, and D. Shen, Emergence of New van Hove Singularities in the Charge Density Wave State of a Topological Kagome Metal RbV3Sb5, Phys. Rev. Lett. 127, 236401 (2021).
  45. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.5.L012017 for NMR/NQR methods on RbV3Sb5 single crystal and computational details, which includes Refs. [16, 33, 47, 48, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60].
  46. I. R. Mukhamedshin, A. V. Dooglav, S. A. Krivenko, and H. Alloul, Evolution of Co charge disproportionation with Na order in NaxCoO2, Phys. Rev. B 90, 115151 (2014).
  47. A. Abragam, The Principles of Nuclear Magnetism (Oxford University Press, 1983).
  48. T. P. Das and E. L. Hahn, Nuclear Quadrupole Resonance Spectroscopy (American Institute of Physics, 1959).
  49. Y. Wang, T. Wu, Z. Li, K. Jiang, and J. Hu, The structure of kagome superconductors av3sb5 in the charge density wave states, arXiv:2210.07585.
  50. 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).
  51. W. G. Clark, M. E. Hanson, and F. Lefloch, Magnetic resonance spectral reconstruction using frequency-shifted and summed Fourier transform processing, Rev. Sci. Instrum. 66, 2453 (1995).
  52. elk code v8.3.25.
  53. M. Methfessel and A. T. Paxton, High-precision sampling for Brillouin-zone integration in metals, Phys. Rev. B 40, 3616 (1989).
  54. J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized Gradient Approximation Made Simple, Phys. Rev. Lett. 77, 3865 (1996).
  55. H. J. Monkhorst and J. D. Pack, Special points for Brillouin-zone integrations, Phys. Rev. B 13, 5188 (1976).
  56. J. D. Pack and H. J. Monkhorst, ”Special points for Brillouin-zone integrations”— a reply, Phys. Rev. B 16, 1748 (1977).
  57. G. Allodi, A. Banderini, R. D. Renzi, and C. Vignali, HyReSpect: A broadband fast-averaging spectrometer for nuclear magnetic resonance of magnetic materials, Rev. Sci. Instrum. 76, 083911 (2005).
  58. E. L. Hahn, Spin echoes, Phys. Rev. 80, 580 (1950).
  59. D. M. S. Bagguley, Pulsed Magnetic Resonance - NMR, ESR, and Optics: A Recognition of E. L. Hahn (Oxford University Press, 1992).
  60. R. E. Wasylishen, NMR Of Quadrupolar Nuclei In Solid Materials (Wiley, 2012).

Outline

Information

Phys. Rev. Research 5, L012017– Published 10 February, 2023
  • Received 20 October 2022
  • Revised 21 December 2022
  • Accepted 18 January 2023
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation