Twofold van hove singularity and origin of charge order in topological kagome superconductor csv3sb5

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 _d__xz_/_d__yz_ kagome band and the p-type vHS of the _d__xy_/_d__x_2–_y_2 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. Access through your institution Buy or subscribe This

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KAGOME SUPERCONDUCTOR CSV3SB5 Article Open access 25 April 2022 CHARGE ORDER LANDSCAPE AND COMPETITION WITH SUPERCONDUCTIVITY IN KAGOME METALS Article 03 November 2022 THREE-DIMENSIONAL

ENERGY GAP AND ORIGIN OF CHARGE-DENSITY WAVE IN KAGOME SUPERCONDUCTOR KV3SB5 Article Open access 11 May 2022 DATA AVAILABILITY Source data are available at

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Google Scholar  * Blochl, P. E. Projector augmented-wave method. _Phys. Rev. B_ 50, 17953–17979 (1994). Article  ADS  Google Scholar  Download references 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). AUTHOR INFORMATION AUTHORS AND AFFILIATIONS

* Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA Mingu Kang & Riccardo Comin * 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 * Department of Physics and Astronomy, Center for Materials Theory, Rutgers University,

Piscataway, NJ, USA Shiang Fang * Department of Physics, Pohang University of Science and Technology, Pohang, Republic of Korea Jeong-Kyu Kim, Jonggyu Yoo & Jae-Hoon Park * Materials

Department and California Nanosystems Institute, University of California Santa Barbara, Santa Barbara, CA, USA Brenden R. Ortiz & Stephen D. Wilson * Advanced Light Source, E. O.

Lawrence Berkeley National Laboratory, Berkeley, CA, USA Sae Hee Ryu, Chris Jozwiak, Aaron Bostwick & Eli Rotenberg * Center for Artificial Low Dimensional Electronic Systems, Institute

for Basic Science (IBS), Pohang, Republic of Korea Jimin Kim * Institut für Theoretische Physik und Astrophysik and Würzburg-Dresden Cluster of Excellence ct.qmat, Universität Würzburg,

Würzburg, Germany Giorgio Sangiovanni * Department of Physics and Astronomy, Alma Mater Studiorum, University of Bologna, Bologna, Italy Domenico Di Sante * Center for Computational Quantum

Physics, Flatiron Institute, New York, NY, USA Domenico Di Sante * Pohang Accelerator Laboratory, Pohang University of Science and Technology, Pohang, Republic of Korea Byeong-Gyu Park *

Department of Physics, Harvard University, Cambridge, MA, USA Efthimios Kaxiras * John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA Efthimios

Kaxiras Authors * Mingu Kang View author publications You can also search for this author inPubMed Google Scholar * Shiang Fang View author publications You can also search for this author

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Park View author publications You can also search for this author inPubMed Google Scholar * Chris Jozwiak View author publications You can also search for this author inPubMed Google

Scholar * Aaron Bostwick View author publications You can also search for this author inPubMed Google Scholar * Eli Rotenberg View author publications You can also search for this author

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You can also search for this author inPubMed Google Scholar 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. CORRESPONDING AUTHORS Correspondence to Mingu Kang, Jae-Hoon Park or Riccardo

Comin. 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. 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 _k__x_-_k__z_ 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_-_k__x_ map of CsV3Sb5 measured at _k__z_ = 5.4 Å-1. C, Representative _E_-_k__z_ map of CsV3Sb5 measured at _k__x_ = 0 Å−1. In c, the energy of the

G-band oscillates as a function of _k__z_, with the periodicity following the three-dimensional Brillouin zone of CsV3Sb5. D-H, Dispersion of the _G_-band at selected _k__z_ 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 _k__z_, while the black arrows in d-h indicate two-dimensional

surface state independent of _k__z_. At _k__z_ = A, the bulk band merges with the surface state. The experimental _k__z_-dependence of _G_-band is highly consistent with the DFT band

structure in Fig. 1g. EXTENDED DATA FIG. 4 _K__Z_-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 _k__z_ ≈ π/c and _k__z_ ≈ 0, respectively.

The vHS from _K1_-band (coral arrow) strongly disperses with _k__z_ 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 _k__z_. 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 _K__Z_ DEPENDENCE OF THE FERMI SURFACE OF CSV3SB5. RIGHTS AND PERMISSIONS Reprints and permissions ABOUT THIS ARTICLE CITE THIS ARTICLE 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 Download citation *

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