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

Nature Physics volume 18, pages 301–308 (2022)Cite this article

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Abstract

The layered vanadium antimonides AV3Sb5 (A = K, Rb, Cs) are a recently discovered family of topological kagome metals that exhibit a range of strongly correlated electronic phases including charge order and superconductivity. However, it is not yet understood how the distinctive electronic structure of the kagome lattice is linked to the observed many-body phenomena. Here we combine angle-resolved photoemission spectroscopy and density functional theory to reveal multiple kagome-derived van Hove singularities (vHS) coexisting near the Fermi level of CsV3Sb5 and analyse their contribution to electronic symmetry breaking. The vHS are characterized by two distinct sublattice flavours (p-type and m-type), which originate, respectively, from their pure and mixed sublattice characters. These twofold vHS flavours of the kagome lattice critically determine the pairing symmetry and unconventional ground states emerging in the AV3Sb5 series. We establish that, among the multiple vHS in CsV3Sb5, the m-type vHS of the dxz/dyz kagome band and the p-type vHS of the dxy/dx2–y2 kagome band are located very close to the Fermi level, setting the stage for electronic symmetry breaking. The former band is characterized by pronounced Fermi surface nesting, while the latter exhibits a higher-order vHS. Our work reveals the essential role of kagome-derived vHS for the collective phenomena realized in the AV3Sb5 family.

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Fig. 1: Theoretical electronic structure and charge order in kagome metal CsV3Sb5.
Fig. 2: Experimental electronic band structure of CsV3Sb5.
Fig. 3: Mapping multiple vHS in CsV3Sb5.
Fig. 4: Fermi surface nesting and charge order gap in the K2′ band.
Fig. 5: Higher-order vHS and charge order gap in the K1 band.

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Data availability

Source data are available at https://doi.org/10.7910/DVN/ZFQIJR. Other data that support the findings of this study are available from the corresponding author upon reasonable request.

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Acknowledgements

We thank S. Jung for fruitful discussions. This work was supported by the Air Force Office of Scientific Research Young Investigator Program under grant FA9550-19-1-0063, and by the STC Center for Integrated Quantum Materials (NSF grant no. DMR-1231319). Work at Max Planck POSTECH Korea Research Initiative was supported by the National Research Foundation of Korea, Ministry of Science (grant no. 2016K1A4A4A01922028). B.R.O. and S.D.W. were supported by the National Science Foundation (NSF) through Enabling Quantum Leap: Convergent Accelerated Discovery Foundries for Quantum Materials Science, Engineering and Information (Q-AMASE-i): Quantum Foundry at UC Santa Barbara (DMR-1906325). This research used resources of the Advanced Light Source, a US DOE Office of Science User Facility under contract no. DE-AC02-05CH11231. M.K. acknowledges a Samsung Scholarship from the Samsung Foundation of Culture. S.F. acknowledges support from a Rutgers Center for Material Theory Distinguished Postdoctoral Fellowship. B.R.O. acknowledges support from the California NanoSystems Institute through the Elings Fellowship programme. The research leading to these results has received funding from the European Union Horizon 2020 research and innovation programme under Marie Skłodowska-Curie grant agreement no. 897276. G.S. is grateful for funding support from the Deutsche Forschungsgemeinschaft (DFG) under Germany’s Excellence Strategy through the Würzburg-Dresden Cluster of Excellence on Complexity and Topology in Quantum Matter ct.qmat (EXC 2147, project ID 390858490) as well as through the Collaborative Research Center SFB 1170 ToCoTronics (project ID 258499086).

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Authors and Affiliations

  1. Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA

    Mingu Kang & Riccardo Comin

  2. Max Planck POSTECH Korea Research Initiative, Center for Complex Phase of Materials, Pohang, Republic of Korea

    Mingu Kang, Jeong-Kyu Kim, Jonggyu Yoo & Jae-Hoon Park

  3. Department of Physics and Astronomy, Center for Materials Theory, Rutgers University, Piscataway, NJ, USA

    Shiang Fang

  4. Department of Physics, Pohang University of Science and Technology, Pohang, Republic of Korea

    Jeong-Kyu Kim, Jonggyu Yoo & Jae-Hoon Park

  5. Materials Department and California Nanosystems Institute, University of California Santa Barbara, Santa Barbara, CA, USA

    Brenden R. Ortiz & Stephen D. Wilson

  6. Advanced Light Source, E. O. Lawrence Berkeley National Laboratory, Berkeley, CA, USA

    Sae Hee Ryu, Chris Jozwiak, Aaron Bostwick & Eli Rotenberg

  7. Center for Artificial Low Dimensional Electronic Systems, Institute for Basic Science (IBS), Pohang, Republic of Korea

    Jimin Kim

  8. Institut für Theoretische Physik und Astrophysik and Würzburg-Dresden Cluster of Excellence ct.qmat, Universität Würzburg, Würzburg, Germany

    Giorgio Sangiovanni

  9. Department of Physics and Astronomy, Alma Mater Studiorum, University of Bologna, Bologna, Italy

    Domenico Di Sante

  10. Center for Computational Quantum Physics, Flatiron Institute, New York, NY, USA

    Domenico Di Sante

  11. Pohang Accelerator Laboratory, Pohang University of Science and Technology, Pohang, Republic of Korea

    Byeong-Gyu Park

  12. Department of Physics, Harvard University, Cambridge, MA, USA

    Efthimios Kaxiras

  13. John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA

    Efthimios Kaxiras

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Contributions

M.K., J.-H.P. and R.C. conceived the project. M.K., J.-K.K., S.H.R. and J.K. performed the ARPES experiments and analysed the resulting data with help from J.Y., C.J., A.B., E.R. and B.-G.P. S.F., G.S. and D.D.S. performed the theoretical calculations with help from E.K. B.R.O. and S.D.W. synthesized and characterized the crystals. M.K., J.-H.P. and R.C. wrote the manuscript with input from all co-authors.

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Correspondence to Mingu Kang, Jae-Hoon Park or Riccardo Comin.

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Extended data

Extended Data Fig. 1 Fermi surface nesting and 2 × 2 charge order in the kagome lattice at the vHs filling.

a, Nesting wave vector of the kagome Fermi surface (red hexagon) at the vHs filling. The nesting vector (green arrows) is equivalent to the (π, 0) (orange arrow) up to a reciprocal lattice vector (black arrows). b, The resulting (π, 0) nesting instability folds the original Brillouin zone (black hexagon) to the new Brillouin zone (dotted blue hexagons), in agreement with the expected momentum-space reconstruction induced by 2 × 2 charge order.

Extended Data Fig. 2 Polarization-dependent ARPES spectra in CsV3Sb5 along the \({{{\bar{\mathrm {\Gamma}}}}}\)-\({{{\bar{\mathrm K}}}}\) (a,b) and \({{{\bar{\mathrm {\Gamma}}}}}\)-\({{{\bar{\mathrm M}}}}\) (c,d) high-symmetry directions.

Data in a,b are acquired with 123 eV photons while those in c,d are acquired with 92 eV photons. It is noticeable that the K2- and K2’-bands manifest exclusively in opposite polarization channels: the K2- (K2’-) band is only visible with linear horizontal (vertical) polarization. The distinct matrix elements for the K2- and K2’-bands may originate from the opposite mirror parity of the basis orbital as discussed in the main text.

Extended Data Fig. 3 Photon-energy dependent ARPES spectra of CsV3Sb5.

a, Representative kx-kz map of CsV3Sb5 measured at a binding energy –0.5 eV. The data is obtained from wide photon-energy dependent measurements from Eph = 70 eV to 200 eV. b, Representative E-kx map of CsV3Sb5 measured at kz = 5.4 Å-1. c, Representative E-kz map of CsV3Sb5 measured at kx = 0 Å−1. In c, the energy of the G-band oscillates as a function of kz, with the periodicity following the three-dimensional Brillouin zone of CsV3Sb5. d-h, Dispersion of the G-band at selected kz coordinates corresponding to the high-symmetry points Γ(e,g) and A (d,f,h). The orange arrows in e,g indicate the bulk band dispersing in kz, while the black arrows in d-h indicate two-dimensional surface state independent of kz. At kz = A, the bulk band merges with the surface state. The experimental kz-dependence of G-band is highly consistent with the DFT band structure in Fig. 1g.

Extended Data Fig. 4 kz-dependence of the vHs.

a-d, vHs of the K1- and K2-bands measured along the \({{{\bar{\mathrm K}}}}\)-\({{{\bar{\mathrm M}}}}\)-\({{{\bar{\mathrm K}}}}\) direction at Eph = 88 eV, 97 eV, 102 eV, and 106 eV respectively. Eph = 97 eV and 106 eV roughly correspond to kz ≈ π/c and kz ≈ 0, respectively. The vHS from K1-band (coral arrow) strongly disperses with kz and crosses EF near 102 eV. In contrast, the vHs from K2-band (dark blue arrow) is mostly two-dimensional and stays below EF at all kz. e-g, vHs of the K2’- and K2-bands measured along \({{{\bar{\mathrm {\Gamma}}}}}\)-\({{{\bar{\mathrm M}}}}\)-\({{{\bar{\mathrm {\Gamma}}}}}\) direction at 83 eV, 88 eV, and 97 eV respectively.

Supplementary information

Supplementary Information

Photon-energy-dependent ARPES studies, and Supplementary Figs. 1–5, Table 1 and References.

Supplementary Video 1 kz dependence of the Fermi surface of CsV3Sb5.

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Kang, M., Fang, S., Kim, JK. et al. Twofold van Hove singularity and origin of charge order in topological kagome superconductor CsV3Sb5. Nat. Phys. 18, 301–308 (2022). https://doi.org/10.1038/s41567-021-01451-5

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