Syozi, I. Statistics of kagome lattice. Prog. Theor. Phys. 6, 306–308 (1951).

Article 
ADS 
MathSciNet 

Google Scholar
 

Balents, L. Spin liquids in frustrated magnets. Nature 464, 199–208 (2010).

Article 
ADS 

Google Scholar
 

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

Article 
ADS 

Google Scholar
 

Mielke, A. Ferromagnetism in the Hubbard model on line graphs and further considerations. J. Phys. A 24, 3311–3321 (1991).

Article 
ADS 
MathSciNet 

Google Scholar
 

Tanaka, A. & Ueda, H. Stability of ferromagnetism in the Hubbard model on the kagome lattice. Phys. Rev. Lett. 90, 067204 (2003).

Article 
ADS 

Google Scholar
 

Yu, S.-L. & Li, J.-X. Chiral superconducting phase and chiral spin-density-wave phase in a Hubbard model on the kagome lattice. Phys. Rev. B 85, 144402 (2012).

Article 
ADS 

Google Scholar
 

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

Article 
ADS 

Google Scholar
 

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

Article 
ADS 

Google Scholar
 

Norman, M. R. Colloquium: Herbertsmithite and the search for the quantum spin liquid. Rev. Mod. Phys. 88, 041002 (2016).

Article 
ADS 
MathSciNet 

Google Scholar
 

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

Article 
ADS 

Google Scholar
 

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).

Article 
ADS 

Google Scholar
 

Liu, T. Strain-induced pseudomagnetic field and quantum oscillations in kagome crystals. Phys. Rev. B 102, 045151 (2020).

Article 
ADS 

Google Scholar
 

Wang, J. et al. Controlled frustration release on the kagome lattice by uniaxial-strain tuning. Phys. Rev. Lett. 131, 256501 (2023).

Article 
ADS 

Google Scholar
 

Lima, W. P., da Costa, D. R., Sena, S. H. R. & Pereira, J. M. Effects of uniaxial and shear strains on the electronic spectrum of Lieb and kagome lattices. Phys. Rev. B 108, 125433 (2023).

Article 
ADS 

Google Scholar
 

Dey, M., Maiti, S. K. & Karmakar, S. N. Magnetic field induced metal-insulator transition in a kagome nanoribbon. J. Appl. Phys. 110, 094306 (2011).

Article 
ADS 

Google Scholar
 

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

Article 
ADS 

Google Scholar
 

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

Article 

Google Scholar
 

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

Article 
ADS 

Google Scholar
 

Tan, H., Liu, Y., Wang, Z. & Yan, B. Charge density waves and electronic properties of superconducting kagome metals. Phys. Rev. Lett. 127, 046401 (2021).

Article 
ADS 

Google Scholar
 

Christensen, M. H., Birol, T., Andersen, B. M. & Fernandes, R. M. Theory of the charge density wave in AV3Sb5 kagome metals. Phys. Rev. B 104, 214513 (2021).

Article 
ADS 

Google Scholar
 

Park, T., Ye, M. & Balents, L. Electronic instabilities of kagome metals: saddle points and Landau theory. Phys. Rev. B 104, 035142 (2021).

Article 
ADS 

Google Scholar
 

Lin, Y.-P. & Nandkishore, R. M. Complex charge density waves at Van Hove singularity on hexagonal lattices: Haldane-model phase diagram and potential realization in the kagome metals AV3Sb5 (A=K, Rb, Cs). Phys. Rev. B 104, 045122 (2021).

Article 
ADS 

Google Scholar
 

Denner, M. M., Thomale, R. & Neupert, T. Analysis of charge order in the kagome metal AV3Sb5 (A = K, Rb, Cs). Phys. Rev. Lett. 127, 217601 (2021).

Article 
ADS 

Google Scholar
 

Christensen, M. H., Birol, T., Andersen, B. M. & Fernandes, R. M. Loop currents in AV3Sb5 kagome metals: multipolar and toroidal magnetic orders. Phys. Rev. B 106, 144504 (2022).

Article 
ADS 

Google Scholar
 

Wagner, G., Guo, C., Moll, P. J. W., Neupert, T. & Fischer, M. H. Phenomenology of bond and flux orders in kagome metals. Phys. Rev. B 108, 125136 (2023).

Article 
ADS 

Google Scholar
 

Tazai, R., Yamakawa, Y. & Kontani, H. Drastic magnetic-field-induced chiral current order and emergent current-bond-field interplay in kagome metals. Proc. Natl Acad. Sci. USA 121, e2303476121 (2024).

Article 
MathSciNet 

Google Scholar
 

Mielke, C. et al. Time-reversal symmetry-breaking charge order in a kagome superconductor. Nature 602, 245–250 (2022).

Article 
ADS 

Google Scholar
 

Khasanov, R. et al. Time-reversal symmetry broken by charge order in CsV3Sb5. Phys. Rev. Res. 4, 023244 (2022).

Article 

Google Scholar
 

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

Article 
ADS 

Google Scholar
 

Xing, Y. et al. Optical manipulation of the charge-density-wave state in RbV3Sb5. Nature 631, 60–66 (2024).

Article 
ADS 

Google Scholar
 

Guo, C. et al. Switchable chiral transport in charge-ordered kagome metal CsV3Sb5. Nature 611, 461–466 (2022).

Article 
ADS 

Google Scholar
 

Wei, X. et al. Three-dimensional hidden phase probed by in-plane magnetotransport in kagome metal CsV3Sb5 thin flakes. Nat. Commun. 15, 5038 (2024).

Article 
ADS 

Google Scholar
 

Guo, C. et al. Correlated order at the tipping point in the kagome metal CsV3Sb5. Nat. Phys. 20, 579–584 (2024).

Article 

Google Scholar
 

Xu, Y. et al. Three-state nematicity and magneto-optical Kerr effect in the charge density waves in kagome superconductors. Nat. Phys. 18, 1470–1475 (2022).

Article 

Google Scholar
 

Farhang, C., Wang, J., Ortiz, B. R., Wilson, S. D. & Xia, J. Unconventional specular optical rotation in the charge ordered state of kagome metal CsV3Sb5. Nat. Commun. 14, 5326 (2023).

Article 
ADS 

Google Scholar
 

Saykin, D. R. et al. High resolution polar Kerr effect studies of CsV3Sb5: tests for time-reversal symmetry breaking below the charge-order transition. Phys. Rev. Lett. 131, 016901 (2023).

Article 
ADS 

Google Scholar
 

Wang, J., Farhang, C., Ortiz, B. R., Wilson, S. D. & Xia, J. Resolving the discrepancy between MOKE measurements at 1550-nm wavelength on kagome metal CsV3Sb5. Phys. Rev. Mater. 8, 014202 (2024).

Article 

Google Scholar
 

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

Article 
ADS 

Google Scholar
 

Xiang, Y. et al. Twofold symmetry of c-axis resistivity in topological kagome superconductor CsV3Sb5 with in-plane rotating magnetic field. Nat. Commun. 12, 6727 (2021).

Article 
ADS 

Google Scholar
 

Jin, F. et al. π phase interlayer shift and stacking fault in the kagome superconductor CsV3Sb5. Phys. Rev. Lett. 132, 066501 (2024).

Article 
ADS 

Google Scholar
 

Liu, Z. et al. Absence of E2g nematic instability and dominant A1g response in the kagome metal CsV3Sb5. Phys. Rev. X 14, 031015 (2024).


Google Scholar
 

Wulferding, D. et al. Emergent nematicity and intrinsic versus extrinsic electronic scattering processes in the kagome metal CsV3Sb5. Phys. Rev. Res. 4, 023215 (2022).

Article 

Google Scholar
 

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

Article 
ADS 

Google Scholar
 

Chen, H. et al. Roton pair density wave in a strong-coupling kagome superconductor. Nature 599, 222–228 (2021).

Article 
ADS 

Google Scholar
 

Li, H. et al. Rotation symmetry breaking in the normal state of a kagome superconductor KV3Sb5. Nat. Phys. 18, 265–270 (2022).

Article 

Google Scholar
 

Asaba, T. et al. Evidence for an odd-parity nematic phase above the charge-density-wave transition in a kagome metal. Nat. Phys. 20, 40–46 (2024).

Article 

Google Scholar
 

Huang, J. et al. Angle-resolved photoemission spectroscopy with an in situ tunable magnetic field. Rev. Sci. Instrum. 94, 093902 (2023).

Article 
ADS 

Google Scholar
 

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

Article 
ADS 

Google Scholar
 

Sobota, J. A., He, Y. & Shen, Z.-X. Angle-resolved photoemission studies of quantum materials. Rev. Mod. Phys. 93, 025006 (2021).

Article 
ADS 

Google Scholar
 

Liu, Z. et al. Charge-density-wave-induced bands renormalization and energy gaps in a kagome superconductor RbV3Sb5. Phys. Rev. X 11, 041010 (2021).


Google Scholar
 

Luo, H. et al. Electronic nature of charge density wave and electron-phonon coupling in kagome superconductor KV3Sb5. Nat. Commun. 13, 273 (2022).

Article 
ADS 

Google Scholar
 

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

Article 

Google Scholar
 

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

Article 
ADS 

Google Scholar
 

Ryu, S. H. et al. magnetoARPES: angle resolved photoemission spectroscopy with magnetic field control. J. Electron Spectrosc. Relat. Phenom. 266, 147357 (2023).

Article 

Google Scholar
 

Ebert, H., Ködderitzsch, D. & Minár, J. Calculating condensed matter properties using the KKR-Green’s function method—recent developments and applications. Rep. Prog. Phys. 74, 096501 (2011).

Article 
ADS 

Google Scholar
 

Ritz, E. T. et al. Superconductivity from orbital-selective electron-phonon coupling in AV3Sb5. Phys. Rev. B 108, L100510 (2023).

Article 
ADS 

Google Scholar
 

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

Article 

Google Scholar
 

Qian, T. et al. Revealing the competition between charge density wave and superconductivity in CsV3Sb5 through uniaxial strain. Phys. Rev. B 104, 144506 (2021).

Article 
ADS 

Google Scholar
 

Kresse, G. & Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 54, 11169–11186 (1996).

Article 
ADS 

Google Scholar
 

Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865 (1996); erratum 78, 1396 (1997).

Vosko, S. H., Wilk, L. & Nusair, M. Accurate spin-dependent electron liquid correlation energies for local spin density calculations: a critical analysis. Can. J. Phys. 58, 1200–1211 (1980).

Article 
ADS 

Google Scholar
 

Rundgren, J. & Malmstrom, J. Transmission and reflection of low-energy electrons at the surface barrier of a metal. J. Phys. C 10, 4671 (1977).

Article 
ADS 

Google Scholar
 

Braun, J. The theory of angle-resolved ultraviolet photoemission and its applications to ordered materials. Rep. Prog. Phys. 59, 1267 (1996).

Article 
ADS 

Google Scholar
 

Guo, H.-M. & Franz, M. Topological insulator on the kagome lattice. Phys. Rev. B 80, 113102 (2009).

Article 
ADS 

Google Scholar