Skip to main content

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.

  • Article
  • Published:

Non-trivial band topology and orbital-selective electronic nematicity in a titanium-based kagome superconductor

Nature Physics volume 19, pages 1827–1833 (2023)Cite this article

Subjects

Abstract

Electronic nematicity that spontaneously breaks rotational symmetry is a generic phenomenon in correlated quantum systems including high-temperature superconductors and the AV3Sb5 (A can be K, Rb or Cs) family of kagome superconductors. However, the underlying mechanism of nematicity in these systems is hard to identify because of its entanglement with other ordered phases. Recently, a family of titanium-based kagome superconductors ATi3Bi5 have been synthesized, where electronic nematicity occurs in the absence of charge order. It provides a platform to study nematicity in its pure form, as well as its interplay with orbital degrees of freedom. Here we reveal the band topology and orbital characters of the multiorbital RbTi3Bi5. We use polarization-dependent angle-resolved photoemission spectroscopy with density functional theory to identify the coexistence of flat bands, type-II Dirac nodal lines and non-trivial topology in this compound. Our study demonstrates the change in orbital character along the Fermi surface contributed by the kagome bands, implying a strong intrinsic interorbital coupling in the Ti-based kagome metals. Furthermore, doping-dependent measurements uncover the orbital-selective features in the kagome bands, which can be explained by d–p hybridization. Hence, interorbital coupling together with d–p hybridization is probably the origin of electronic nematicity in ATi3Bi5.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Crystal structure and calculated band structure of RbTi3Bi5.
Fig. 2: Polarization-dependent measurements of the kagome bands.
Fig. 3: ℤ2 topological surface states in RbTi3Bi5.
Fig. 4: Orbital-selective doping effect and d–p hybridization in RbTi3Bi5.

Similar content being viewed by others

Data availability

All data needed to evaluate the conclusions in the paper are present in the paper and/or the Supplementary Information. All other data that support the findings of this study are available from the corresponding authors upon reasonable request. Source data are provided with this paper.

Code availability

The band structures used in this study are available from the corresponding authors upon reasonable request.

References

  1. Chuang, T.-M. et al. Nematic electronic structure in the ‘parent’ state of the iron-based superconductor Ca(Fe1–xCox)2As2. Science 327, 181–184 (2010).

    ADS  Google Scholar 

  2. Chu, J.-H. et al. In-plane resistivity anisotropy in an underdoped iron arsenide superconductor. Science 329, 824–826 (2010).

    ADS  Google Scholar 

  3. Chu, J.-H., Kuo, H.-H., Analytis, J. G. & Fisher, I. R. Divergent nematic susceptibility in an iron arsenide superconductor. Science 337, 710–712 (2012).

    ADS  Google Scholar 

  4. Rosenthal, E. P. et al. Visualization of electron nematicity and unidirectional antiferroic fluctuations at high temperatures in NaFeAs. Nat. Phys. 10, 225–232 (2014).

    Google Scholar 

  5. Kuo, H.-H., Chu, J.-H., Palmstrom, J. C., Kivelson, S. A. & Fisher, I. R. Ubiquitous signatures of nematic quantum criticality in optimally doped Fe-based superconductors. Science 352, 958–962 (2016).

    ADS  MathSciNet  MATH  Google Scholar 

  6. Ando, Y., Segawa, K., Komiya, S. & Lavrov, A. N. Electrical resistivity anisotropy from self-organized one dimensionality in high-temperature superconductors. Phys. Rev. Lett. 88, 137005 (2002).

    ADS  Google Scholar 

  7. Hinkov, V. et al. Electronic liquid crystal state in the high-temperature superconductor YBa2Cu3O6.45. Science 319, 597–600 (2008).

    Google Scholar 

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

    ADS  Google Scholar 

  9. Daou, R. et al. Broken rotational symmetry in the pseudogap phase of a high-Tc superconductor. Nature 463, 519–522 (2010).

    ADS  Google Scholar 

  10. Fernandes, R., Chubukov, A. & Schmalian, J. What drives nematic order in iron-based superconductors? Nat. Phys. 10, 97–104 (2014).

    Google Scholar 

  11. Keimer, B. et al. From quantum matter to high-temperature superconductivity in copper oxides. Nature 518, 179–186 (2015).

    ADS  Google Scholar 

  12. Kiesel, M. L. & Thomale, R. Sublattice interference in the kagome Hubbard model. Phys. Rev. B 86, 121105(R) (2012).

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  14. 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).

    ADS  Google Scholar 

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

    Google Scholar 

  16. Wu, X. et al. Nature of unconventional pairing in the kagome superconductors AV3Sb5. Phys. Rev. Lett. 127, 177001 (2021).

    ADS  Google Scholar 

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

    ADS  Google Scholar 

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

    Google Scholar 

  19. Hu, Y. et al. Rich nature of Van Hove singularities in kagome superconductor CsV3Sb5. Nat. Commun. 13, 2220 (2022).

    ADS  Google Scholar 

  20. 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).

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  22. Han, T., Chu, S. & Lee, Y. S. Refining the spin Hamiltonian in the spin-1/2 kagome lattice antiferromagnet ZnCu3(OH)6Cl2 using single crystals. Phys. Rev. Lett. 108, 157202 (2012).

    ADS  Google Scholar 

  23. Fu, M., Imai, T., Han, T.-H. & Lee, Y. S. Evidence for a gapped spin-liquid ground state in a kagome Heisenberg antiferromagnet. Science 350, 655–658 (2015).

    ADS  Google Scholar 

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

    Google Scholar 

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

    ADS  Google Scholar 

  26. Liu, D.-F. et al. Magnetic Weyl semimetal phase in a kagome crystal. Science 365, 1282–1285 (2019).

    ADS  Google Scholar 

  27. Ko, W.-H., Lee, P. A. & Wen, X.-G. Doped kagome system as exotic superconductor. Phys. Rev. B 79, 214502 (2009).

    ADS  Google Scholar 

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

    Google Scholar 

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

    ADS  Google Scholar 

  30. Chen, H. et al. Roton pair density wave and unconventional strong-coupling superconductivity in a topological kagome metal. Nature 559, 222–228 (2021).

    ADS  Google Scholar 

  31. Jiang, Y.-X. et al. Discovery of unconventional chiral charge order in kagome superconductor KV3Sb5. Nat. Mater. 20, 1353–1357 (2021).

    ADS  Google Scholar 

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

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  34. Yang, H. et al. Titanium-based kagome superconductor CsTi3Bi5 and topological states. Preprint at https://arxiv.org/abs/2209.03840 (2022).

  35. Werhahn, D. et al. The kagomé metals RbTi3Bi5 and CsTi3Bi5. Z. Naturforsch. B 77, 757–764 (2022).

  36. Yang, H. et al. Superconductivity and orbital-selective nematic order in a new titanium-based kagome metal CsTi3Bi5. Preprint at https://arxiv.org/abs/2211.12264 (2022).

  37. Li, H. et al. Electronic nematicity in the absence of charge density waves in a new titanium-based kagome metal. Nat. Phys. https://doi.org/10.1038/s41567-023-02176-3 (2023).

  38. Damascelli, A., Hussain, Z. & Shen, Z.-X. Angle-resolved photoemission studies of the cuprate superconductors. Rev. Mod. Phys. 75, 473–541 (2003).

    ADS  Google Scholar 

  39. Yi, X.-W. et al. Large kagome family candidates with topological superconductivity and charge density waves. Phys. Rev. B 106, L220505 (2022).

    ADS  Google Scholar 

  40. Jiang, Y. et al. Screening promising CsV3Sb5-like kagome materials from systematic first-principles evaluation. Chinese Phys. Lett. 39, 047402 (2022).

    ADS  Google Scholar 

  41. Hecher, M. & Schmalian, J. Vestigial nematic order and superconductivity in the doped topological insulator CuxBi2Se3. npj Quantum Mater. 3, 26 (2018).

    ADS  Google Scholar 

  42. Fernandes, R. M., Orth, P. P. & Schmalian, J. Intertwined vestigial order in quantum materials: nematicity and beyond. Annu. Rev. Condens. Matter Phys. 10, 133–154 (2019).

    ADS  Google Scholar 

  43. Jiang, K., Hu, J., Ding, H. & Wang, Z. Interatomic Coulomb interaction and electron nematic bond order in FeSe. Phys. Rev. B 93, 115138 (2016).

    ADS  Google Scholar 

  44. Kresse, G. & Hafner, J. Ab initio molecular dynamics for liquid metals. Phys. Rev. B 47, 558 (1993).

    ADS  Google Scholar 

  45. 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 (1996).

    Google Scholar 

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

    ADS  Google Scholar 

  47. Monkhorst, H. J. & Pack, J. D. Special points for Brillouin-zone integrations. Phys. Rev. B 13, 5188 (1976).

    ADS  MathSciNet  Google Scholar 

  48. Mostofi, A. A. et al. wannier90: a tool for obtaining maximally-localised Wannier functions. Comput. Phys. Commun. 178, 685 (2008).

    ADS  MATH  Google Scholar 

  49. Lopez Sancho, M. P., Lopez Sancho, J. M., Sancho, J. M. L. & Rubio, J. Highly convergent schemes for the calculation of bulk and surface Green functions. J. Phys. F: Met. Phys. 15, 851 (1985).

    ADS  Google Scholar 

Download references

Acknowledgements

Work at the Paul Scherrer Institut was supported by the Swiss National Science Foundation under grant no. 200021_188413. X.W. was supported by the National Natural Science Foundation of China (grant no. 12047503). J.M. was supported by the Research Grants Council of Hong Kong via Early Career Scheme (21304023), the Collaborative Research Fund (C6033-22G), the Collaborative Research Equipment Grant (C1018-22E) and the National Natural Science Foundation of China (12104379). J.H. was supported by the Ministry of Science and Technology (grant no. 2022YFA1403901), the National Natural Science Foundation of China (grant no. NSFC-11888101) and the New Cornerstone Foundation.

Author information

Author notes

  1. These authors contributed equally: Yong Hu, Congcong Le, Yuhang Zhang.

Authors and Affiliations

  1. Photon Science Division, Paul Scherrer Institut, Villigen PSI, Switzerland

    Yong Hu, Nicholas C. Plumb, Milan Radovic & Ming Shi

  2. RIKEN Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS), Wako, Japan

    Congcong Le

  3. Beijing National Center for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing, People’s Republic of China

    Yuhang Zhang, Zhen Zhao, Jiali Liu, Hui Chen, Xiaoli Dong, Jiangping Hu, Haitao Yang & Hong-Jun Gao

  4. School of Physical Sciences, University of Chinese Academy of Sciences, Beijing, People’s Republic of China

    Yuhang Zhang, Zhen Zhao, Jiali Liu, Hui Chen, Xiaoli Dong, Jiangping Hu, Haitao Yang & Hong-Jun Gao

  5. Department of Physics, City University of Hong Kong, Kowloon, People’s Republic of China

    Junzhang Ma

  6. City University of Hong Kong Shenzhen Research Institute, Shenzhen, People’s Republic of China

    Junzhang Ma

  7. Max-Planck-Institut für Festkörperforschung, Stuttgart, Germany

    Andreas P. Schnyder

  8. CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing, People’s Republic of China

    Xianxin Wu

  9. Center for Correlated Matter and Department of Physics, Zhejiang University, Hangzhou, People’s Republic of China

    Ming Shi

Authors
  1. Yong Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Congcong Le
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yuhang Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Zhen Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Jiali Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Junzhang Ma
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Nicholas C. Plumb
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Milan Radovic
    View author publications

    You can also search for this author in PubMed Google Scholar

  9. Hui Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  10. Andreas P. Schnyder
    View author publications

    You can also search for this author in PubMed Google Scholar

  11. Xianxin Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  12. Xiaoli Dong
    View author publications

    You can also search for this author in PubMed Google Scholar

  13. Jiangping Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

  14. Haitao Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  15. Hong-Jun Gao
    View author publications

    You can also search for this author in PubMed Google Scholar

  16. Ming Shi
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

Y.H. and M.S. conceived the ARPES experiments. Z.Z. grew and characterized the crystals with guidance from H.C., H.Y. and H.-J.G. X.W. and C.L. performed the theoretical calculations and analysis with support from A.P.S. and J.H. Y.H. performed the ARPES experiments with help from J.M., M.R. and M.S. Y.Z. and J.L. performed the transport measurements with guidance from X.D. N.C.P. maintained the ARPES facilities at ULTRA, SIS. Y.H. analysed the data. Y.H. and X.W. wrote the paper with inputs from all authors.

Corresponding authors

Correspondence to Yong Hu, Xianxin Wu, Hong-Jun Gao or Ming Shi.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature Physics thanks the anonymous reviewers 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.

Supplementary information

Supplementary Information

Supplementary Sections 1–8 and Figs. 1–8.

Source data

Source Data Fig. 1

Magnetic susceptibilities, temperature-dependent resistivity and DFT-calculated band dispersions of RbTi3Bi5.

Source Data Fig. 2

DFT-calculated electronic structure and ARPES spectra for the flat bands.

Source Data Fig. 4

Doping-dependent EDCs and orbital-resolved DFT-calculated band dispersion.

Rights and permissions

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 permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hu, Y., Le, C., Zhang, Y. et al. Non-trivial band topology and orbital-selective electronic nematicity in a titanium-based kagome superconductor. Nat. Phys. 19, 1827–1833 (2023). https://doi.org/10.1038/s41567-023-02215-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41567-023-02215-z

This article is cited by

Search

Advanced search

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