- Open Access
Machine-learning-guided discovery of kagome superconductors and
Phys. Rev. Research 8, 023308 – Published 17 June, 2026
DOI: https://doi.org/10.1103/lpqj-7hyg
Abstract
We report the experimental discovery of bulk superconductivity in two kagome lattice compounds, and , which were predicted through machine-learning-accelerated high-throughput screening combined with first-principles calculations. These materials crystallize in the hexagonal -type structure with planar kagome networks formed by Ru atoms. We observe superconducting critical temperatures of K for and K for , confirmed through magnetization, specific heat, and electrical transport measurements. Both compounds exhibit nearly 100% superconducting volume fractions, demonstrating bulk superconductivity. Compared with isostructural and show a more dispersive Ru local quasiflat band [and thus a reduced density of states (DOS) at ] together with an overall hardening of the phonon spectrum, both of which lower the electron-phonon coupling (EPC) constant . Meanwhile, the dominant real-space EPC between Ru local states and the low-frequency Ru in-plane local branch remains nearly unchanged, indicating that the reduction of originates from the DOS reduction and the overall phonon hardening. Superfluid weight calculations show that conventional contributions dominate over quantum geometric effects due to the dispersive nature of bands near the Fermi level. This work demonstrates the effectiveness of integrating machine-learning screening, first-principles theory, and experimental synthesis for accelerating the discovery of new superconducting materials.
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References (64)
- M. Tinkham, Introduction to Superconductivity, 2nd ed. (McGraw-Hill, New York, 1996).
- J. Bardeen, L. N. Cooper, and J. R. Schrieffer, Theory of superconductivity, Phys. Rev. 108, 1175 (1957).
- J. G. Bednorz and K. A. Müller, Possible high superconductivity in the Ba-La-Cu-O system, Z. Phys. B 64, 189 (1986).
- Y. Kamihara, T. Watanabe, M. Hirano, and H. Hosono, Iron-based layered superconductor ]FeAs ( = 0.05–0.12) with = 26 K, J. Am. Chem. Soc. 130, 3296 (2008).
- F. Steglich, J. Aarts, C. D. Bredl, W. Lieke, D. Meschede, W. Franz, and H. Schäfer, Superconductivity in the presence of strong Pauli paramagnetism: , Phys. Rev. Lett. 43, 1892 (1979).
- M. R. D. Jérome, A. Mazaud, and K. Bechgaard, Superconductivity in a synthetic organic conductor (TMTSF), J. Phys. Lett. 41, 95 (1980).
- D. Li, K. Lee, B. Y. Wang, M. Osada, S. Crossley, H. R. Lee, Y. Cui, Y. Hikita, and H. Y. Hwang, Superconductivity in an infinite-layer nickelate, Nature (London) 572, 624 (2019).
- D. Li, K. Lee, B. Y. Wang, M. Osada, S. Crossley, H. R. Lee, Y. Cui, Y. Hikita, and H. Y. Hwang, Superconductivity at 39 K in magnesium diboride, Nature (London) 410, 432 (2001).
- N. W. Ashcroft, Metallic hydrogen: A high-temperature superconductor? Phys. Rev. Lett. 21, 1748 (1968).
- N. W. Ashcroft, Hydrogen dominant metallic alloys: High temperature superconductors? Phys. Rev. Lett. 92, 187002 (2004).
- L. Boeri, R. G. Hennig, P. J. Hirschfeld, G. Profeta, A. Sanna, E. Zurek, W. E. Pickett, M. Amsler, R. Dias, M. Eremets, et al., The 2021 room-temperature superconductivity roadmap, J. Phys.: Condens. Matter 34, 183002 (2022).
- K. Gao, T. Cerqueira, A. Sanna, Y.-W. Fang, Đ. Dangić, I. Errea, H.-C. Wang, S. Botti, and M. A. L. Marques, The maximum of conventional superconductors at ambient pressure, Nat. Commun. 16, 8253 (2025).
- J. B. Gibson, A. C. Hire, P. Prakash, P. M. Dee, B. Geisler, J. S. Kim, Z. Li, J. J. Hamlin, G. R. Stewart, P. J. Hirschfeld, and R. G. Hennig, Developing a complete AI-accelerated workflow for superconductor discovery, npj Comput. Mater. 12, 95 (2025).
- J. Deng, Y. Jiang, T. F. T. Cerqueira, H. Hu, E. O. Lamponen, D. Călugăru, Z. W. Hanqi Pi, M. G. Vergniory, E. Morosan, T. Neupert, S. Blanco-Canosa, C. Felser, K. Haule, M. A. L. Marques, P. Törmä, and B. A. Bernevig, Theory of superconductivity in and predictions of new kagome flat band superconductors, arXiv:2503.20867.
- P. Prakash, J. B. Gibson, Z. Li, G. D. Gianluca, J. Esquivel, E. Fuemmeler, B. Geisler, J. S. Kim, A. Roitberg, E. B. Tadmor, M. Liu, S. Martiniani, G. R. Stewart, J. J. Hamlin, P. J. Hirschfeld, and R. G. Hennig, Guided diffusion for the discovery of new superconductors, arXiv:2509.25186.
- O. Lesser, Y. Liu, N. Maus, A. Panigrahi, K. Mallayya, A. Gong, A. Kabra, S. B. Lee, S. Chatterjee, A. Merino, K. Q. Weinberger, L. M. Schoop, J. R. Gardner, and E.-A. Kim, Electron affinity difference distributions guide the discovery of the superconductor , arXiv:2510.07373.
- J. Yu, B. A. Bernevig, R. Queiroz, E. Rossi, P. Törmä, and B.-J. Yang, Quantum geometry in quantum materials, npj Quantum Mater. 10, 101 (2025).
- S. Peotta and P. Törmä, Superfluidity in topologically nontrivial flat bands, Nat. Commun. 6, 8944 (2015).
- P. Törmä, S. Peotta, and B. A. Bernevig, Superconductivity, superfluidity and quantum geometry in twisted multilayer systems, Nat. Rev. Phys. 4, 528 (2022).
- H. Hu, O. Vafek, K. Haule, and B. A. Bernevig, Ferromagnetism vs. antiferromagnetism in narrow-band systems: Competition between quantum geometry and band dispersion, arXiv:2509.03575.
- T. Gaggl, R. Misawa, M. Kriener, Y. Tanaka, R. Yamada, and M. Hirschberger, Bulk superconductivity in the kagome metal , Phys. Scr. 101, 055912 (2026).
- M. J. Winiarski, D. Walczak, S. Królak, D. Yazici, R. J. Cava, and T. Klimczuk, —A kagome lattice superconductor, J. Phys.: Mater. 9, 025013 (2026).
- H. Ku, G. Meisner, F. Acker, and D. Johnston, Superconducting and magnetic properties of new ternary borides with the -type structure, Solid State Commun. 35, 91 (1980).
- K. Hiebl, P. Rogl, E. Uhl, and M. J. Sienko, Magnetic behavior and structural chemistry of borides, Inorg. Chem. 19, 3316 (1980).
- T. Roisnel and J. Rodríguez-Carvajal, Winplotr: A Windows tool for powder diffraction pattern analysis, Mater. Sci. Forum 378–381, 118 (2001).
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/lpqj-7hyg for detailed low temperature heat capacity data and calculations of the superconducting gap on the Fermi surface.
- L. L. Zhao, S. Lausberg, H. Kim, M. A. Tanatar, M. Brando, R. Prozorov, and E. Morosan, Type-I superconductivity in single crystals, Phys. Rev. B 85, 214526 (2012).
- C.-w. Cho, J. H. Yang, N. F. Q. Yuan, J. Shen, T. Wolf, and R. Lortz, Thermodynamic evidence for the Fulde-Ferrell-Larkin-Ovchinnikov state in the superconductor, Phys. Rev. Lett. 119, 217002 (2017).
- S. Ichinokura, Y. Nakata, K. Sugawara, Y. Endo, A. Takayama, T. Takahashi, and S. Hasegawa, Vortex-induced quantum metallicity in the mono-unit-layer superconductor , Phys. Rev. B 99, 220501 (2019).
- R. Joynt and L. Taillefer, The superconducting phases of , Rev. Mod. Phys. 74, 235 (2002).
- D. Aoki, F. Honda, G. Knebel, D. Braithwaite, A. Nakamura, D. Li, Y. Homma, Y. Shimizu, Y. J. Sato, J. P. Brison, and J. Flouquet, Multiple superconducting phases and unusual enhancement of the upper critical field in , J. Phys. Soc. Jpn. 89, 053705 (2020).
- A. Rosuel, C. Marcenat, G. Knebel, T. Klein, A. Pourret, N. Marquardt, Q. Niu, S. Rousseau, A. Demuer, G. Seyfarth, G. Lapertot, D. Aoki, D. Braithwaite, J. Flouquet, and J. P. Brison, Field-induced tuning of the pairing state in a superconductor, Phys. Rev. X 13, 011022 (2023).
- P. E. Blöchl, Projector augmented-wave method, Phys. Rev. B 50, 17953 (1994).
- G. Kresse and D. Joubert, From ultrasoft pseudopotentials to the projector augmented-wave method, Phys. Rev. B 59, 1758 (1999).
- G. Kresse and J. Furthmüller, Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set, Comput. Mater. Sci. 6, 15 (1996).
- G. Kresse and J. Furthmüuller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Phys. Rev. B 54, 11169 (1996).
- J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996).
- H. J. Monkhorst and J. D. Pack, Special points for Brillouin-zone integrations, Phys. Rev. B 13, 5188 (1976).
- J. Gao, Q. Wu, C. Persson, and Z. Wang, Irvsp: To obtain irreducible representations of electronic states in the VASP, Comput. Phys. Commun. 261, 107760 (2021).
- A. A. Mostofi, J. R. Yates, Y.-S. Lee, I. Souza, D. Vanderbilt, and N. Marzari, Wannier90: A tool for obtaining maximally-localised Wannier functions, Comput. Phys. Commun. 178, 685 (2008).
- A. A. Mostofi, J. R. Yates, G. Pizzi, Y.-S. Lee, I. Souza, D. Vanderbilt, and N. Marzari, An updated version of Wannier90: A tool for obtaining maximally-localised Wannier functions, Comput. Phys. Commun. 185, 2309 (2014).
- G. Pizzi, V. Vitale, R. Arita, S. Blügel, F. Freimuth, G. Géranton, M. Gibertini, D. Gresch, C. Johnson, T. Koretsune, et al., Wannier90 as a community code: New features and applications, J. Phys.: Condens. Matter 32, 165902 (2020).
- J. Deng, R. Zhang, Y. Xie, X. Wu, and Z. Wang, Two elementary band representation model, Fermi surface nesting, and surface topological superconductivity in ( = K, Rb, Cs), Phys. Rev. B 108, 115123 (2023).
- Y. Jiang, H. Hu, D. Călugăru, C. Felser, S. Blanco-Canosa, H. Weng, Y. Xu, and B. A. Bernevig, FeGe as a building block for the kagome 1:1, 1:6:6, and 1:3:5 families: Hidden -orbital decoupling of flat band sectors, effective models, and interaction Hamiltonians, Phys. Rev. B 111, 125163 (2025).
- Q. Wu, S. Zhang, H.-F. Song, M. Troyer, and A. A. Soluyanov, WannierTools: An open-source software package for novel topological materials, Comput. Phys. Commun. 224, 405 (2018).
- F. Giustino, M. L. Cohen, and S. G. Louie, Electron-phonon interaction using Wannier functions, Phys. Rev. B 76, 165108 (2007).
- J. Noffsinger, F. Giustino, B. D. Malone, C.-H. Park, S. G. Louie, and M. L. Cohen, EPW: A program for calculating the electron–phonon coupling using maximally localized Wannier functions, Comput. Phys. Commun. 181, 2140 (2010).
- S. Poncé, E. R. Margine, C. Verdi, and F. Giustino, EPW: Electron-phonon coupling, transport and superconducting properties using maximally localized Wannier functions, Comput. Phys. Commun. 209, 116 (2016).
- H. Lee, S. Poncé, K. Bushick, S. Hajinazar, J. Lafuente-Bartolome, J. Leveillee, C. Lian, J.-M. Lihm, F. Macheda, H. Mori, H. Paudyal, W. H. Sio, S. Tiwari, M. Zacharias, X. Zhang, N. Bonini, E. Kioupakis, E. R. Margine, and F. Giustino, Electron-phonon physics from first principles using the EPW code, npj Comput. Mater. 9, 156 (2023).
- P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, G. L. Chiarotti, M. Cococcioni, I. Dabo, et al., QUANTUM ESPRESSO: A modular and open-source software project for quantum simulations of materials, J. Phys.: Condens. Matter 21, 395502 (2009).
- P. Giannozzi, O. Andreussi, T. Brumme, O. Bunau, M. Buongiorno Nardelli, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, M. Cococcioni, et al., Advanced capabilities for materials modelling with Quantum Espresso, J. Phys.: Condens. Matter 29, 465901 (2017).
- J. P. Perdew, A. Ruzsinszky, G. I. Csonka, O. A. Vydrov, G. E. Scuseria, L. A. Constantin, X. Zhou, and K. Burke, Restoring the density-gradient expansion for exchange in solids and surfaces, Phys. Rev. Lett. 100, 136406 (2008).
- M. Van Setten, M. Giantomassi, E. Bousquet, M. Verstraete, D. Hamann, X. Gonze, and G.-M. Rignanese, The PseudoDojo: Training and grading a 85 element optimized norm-conserving pseudopotential table, Comput. Phys. Commun. 226, 39 (2018).
- M. Methfessel and A. T. Paxton, High-precision sampling for Brillouin-zone integration in metals, Phys. Rev. B 40, 3616 (1989).
- P. Kràl, J. N. Graham, V. Sazgari, I. Plokhikh, A. Lukovkina, O. Gerguri, I. Bialo, A. Doll, L. Martinelli, J. Oppliger, et al., Discovery of high-temperature charge order and time-reversal symmetry-breaking in the kagome superconductor , arXiv:2507.06885.
- R. Misawa, S. Kitou, R. Yamada, T. Gaggl, R. Nakano, Y. Shibata, Y. Okamura, M. Kriener, P. R. Baral, Y. Nakamura, Y. Ōnuki, Y. Takahashi, T.-H. Arima, M. Jovanovic, L. M. Schoop, and M. Hirschberger, Successive orthorhombic distortions in kagome metals by molecular orbital formation, Adv. Mater. 38, e13015 (2026).
- M. I. Aroyo, J. M. Perez-Mato, D. Orobengoa, E. Tasci, G. de la Flor, and A. Kirov, Crystallography online: Bilbao Crystallographic Server, Bulg. Chem. Commun. 43, 183 (2011).
- M. I. Aroyo, J. M. Perez-Mato, C. Capillas, E. Kroumova, S. Ivantchev, G. Madariaga, A. Kirov, and H. Wondratschek, Bilbao Crystallographic Server: I. Databases and crystallographic computing programs, Z. Kristallogr. Cryst. Mater. 221, 15 (2006).
- M. I. Aroyo, A. Kirov, C. Capillas, J. Perez-Mato, and H. Wondratschek, Bilbao Crystallographic Server. II. Representations of crystallographic point groups and space groups, Acta Crystallogr. A Found. Crystallogr. 62, 115 (2006).
- W. L. McMillan, Transition temperature of strong-coupled superconductors, Phys. Rev. 167, 331 (1968).
- R. Dynes, McMillan's equation and the of superconductors, Solid State Commun. 10, 615 (1972).
- P. B. Allen and R. C. Dynes, Transition temperature of strong-coupled superconductors reanalyzed, Phys. Rev. B 12, 905 (1975).
- K.-E. Huhtinen, J. Herzog-Arbeitman, A. Chew, B. A. Bernevig, and P. Törmä, Revisiting flat band superconductivity: Dependence on minimal quantum metric and band touchings, Phys. Rev. B 106, 014518 (2022).
- L. Liang, T. I. Vanhala, S. Peotta, T. Siro, A. Harju, and P. Törmä, Band geometry, Berry curvature, and superfluid weight, Phys. Rev. B 95, 024515 (2017).