- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Type-I and type-II saddle points and a quasiflat band in a Bi-pyrochlore superconductor CsBi2

Yusei Morita1,*, Yongkai Li2,3,4,*, Yu-Hao Wei5,*, Kosuke Nakayama1,†, Zhiwei Wang2,3,4,6,‡, Hua-Yu Li5, Takemi Kato7, Seigo Souma7,8, Kiyohisa Tanaka9,10 et al.

Kenichi Ozawa11, Jia-Xin Yin12,13, Takashi Takahashi1, Min-Quan Kuang5,§, Yugui Yao2,3,4,6, and Takafumi Sato1,14,15,7,8,∥

  • *These authors contributed equally to this work.
  • †Contact author: k.nakayama@arpes.phys.tohoku.ac.jp
  • ‡Contact author: zhiweiwang@bit.edu.cn
  • §Contact author: mqkuang@swu.edu.cn
  • ∥Contact author: t-sato@arpes.phys.tohoku.ac.jp
PDF

Phys. Rev. Research 8, 033253 – Published 3 September, 2026

DOI: https://doi.org/10.1103/2ntb-dzck

Abstract

The divergence of the electron density of states (DOS) plays an important role in enhancing many-body interactions and inducing various quantum phases in low-dimensional systems. However, such unique electronic structures remain experimentally elusive in three-dimensional (3D) systems, particularly those with strong spin-orbit coupling (SOC). Using angle-resolved photoemission spectroscopy and first-principles calculations for a Laves-phase superconductor CsBi2, which features a Bi-pyrochlore 3D network with strong SOC, we identify two characteristic electronic structures with a large DOS. One is a quasiflat band within a topologically nontrivial band sector with p-orbital character, locally formed around the U-K line, which enhances DOS near the Fermi level. The other involves type-I and type-II saddle points connected by a quasiflat band, which cooperatively produce an enhancement in the DOS. Our findings lay a foundation for exploring exotic phenomena driven by the interplay of multiple singularities with a large DOS, nontrivial topology, and strong SOC in 3D pyrochlores.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (83)

  1. J. W. G. Wilder, L. C. Venema, A. G. Rinzler, R. E. Smalley, and C. Dekker, Electronic structure of atomically resolved carbon nanotubes, Nature (London) 391, 59 (1998).
  2. T. W. Odom, J.-L. Huang, P. Kim, and C. M. Lieber, Atomic structure and electronic properties of single-walled carbon nanotubes, Nature (London) 391, 62 (1998).
  3. L. Van Hove, The occurrence of singularities in the elastic frequency distribution of a crystal, Phys. Rev. 89, 1189 (1953).
  4. D. S. Dessau, Z.-X. Shen, D. M. King, D. S. Marshall, L. W. Lombardo, P. H. Dickinson, A. G. Loeser, J. DiCarlo, C.-H. Park, A. Kapitulnik, and W. E. Spicer, Key features in the measured band structure of Bi2Sr2CaCu2O8+δ: Flat bands at EF and Fermi surface nesting, Phys. Rev. Lett. 71, 2781 (1993).
  5. K. Gofron, J. C. Campuzano, A. A. Abrikosov, M. Lindroos, A. Bansil, H. Ding, D. Koelling, and B. Dabrowski, Observation of an “extended” van Hove singularity in YBa2Cu4O8 by ultrahigh energy resolution angle-resolved photoemission, Phys. Rev. Lett. 73, 3302 (1994).
  6. S. V. Borisenko, V. B. Zabolotnyy, D. V. Evtushinsky, T. K. Kim, I. V. Morozov, A. N. Yaresko, A. A. Kordyuk, G. Behr, A. Vasiliev, R. Follath, and B. Büchner, Superconductivity without nesting in LiFeAs, Phys. Rev. Lett. 105, 067002 (2010).
  7. A. Tamai, M. P. Allan, J. F. Mercure, W. Meevasana, R. Dunkel, D. H. Lu, R. S. Perry, A. P. Mackenzie, D. J. Singh, Z.-X. Shen, and F. Baumberger, Fermi surface and van Hove singularities in the itinerant metamagnet Sr3Ru2O7, Phys. Rev. Lett. 101, 026407 (2008).
  8. M. Kang, S. Fang, J.-K. Kim, B. R. Ortiz, S. H. Ryu, J. Kim, J. Yoo, G. Sangiovanni, D. D. Sante, B.-G. Park, C. Jozwiak, A. Bostwick, E. Rotenberg, E. Kaxiras, S. D. Wilson, J.-H. Park, and R. Comin, Twofold van Hove singularity and origin of charge order in topological kagome superconductor CsV3Sb5, Nat. Phys. 18, 301 (2022).
  9. Y. Hu, X. Wu, B. R. Ortiz, S. Ju, X. Han, J. Ma, N. C. Plumb, M. Radovic, R. Thomale, S. D. Wilson, A. P. Schnyder, and M. Shi, Rich nature of van Hove singularities in kagome superconductor CsV3Sb5, Nat. Commun. 13, 2220 (2022).
  10. Y. He, S.-D. Chen, Z.-X. Li, D. Zhao, D. Song, Y. Yoshida, H. Eisaki, T. Wu, X.-H. Chen, D.-H. Lu, C. Meingast, T. P. Devereaux, R. J. Birgeneau, M. Hashimoto, D.-H. Lee, and Z.-X. Shen, Superconducting fluctuations in overdoped Bi2Sr2CaCu2O8+δ, Phys. Rev. X 11, 031068 (2021).
  11. D. Fang, X. Shi, Z. Du, P. Richard, H. Yang, X. X. Wu, P. Zhang, T. Qian, X. Ding, Z. Wang, T. K. Kim, M. Hoesch, A. Wang, X. Chen, J. Hu, H. Ding, and H.-H. Wen, Observation of a van Hove singularity and implication for strong-coupling induced Cooper pairing in KFe2As2, Phys. Rev. B 92, 144513 (2015).
  12. G. N. Phan, K. Nakayama, K. Sugawara, T. Sato, T. Urata, Y. Tanabe, K. Tanigaki, F. Nabeshima, Y. Imai, A. Maeda, and T. Takahashi, Effects of strain on the electronic structure, superconductivity, and nematicity in FeSe studied by angle-resolved photoemission spectroscopy, Phys. Rev. B 95, 224507 (2017).
  13. V. Sunko, E. A. Morales, I. Marković, M. E. Barber, D. Milosavljević, F. Mazzola, D. A. Sokolov, N. Kikugawa, C. Cacho, P. Dudin, H. Rosner, C. W. Hicks, P. D. C. King, and A. P. Mackenzie, Direct observation of a uniaxial stress-driven Lifshitz transition in Sr2RuO4, npj Quantum Mater. 4, 46 (2019).
  14. M. E. Barber, A. S. Gibbs, Y. Maeno, A. P. Mackenzie, and C. W. Hicks, Resistivity in the vicinity of a van Hove singularity: Sr2RuO4 under uniaxial pressure, Phys. Rev. Lett. 120, 076602 (2018).
  15. Y.-X. Jiang, J.-X. Yin, M. M. Denner, N. Shumiya, B. R. Ortiz, G. Xu, Z. Guguchia, J. He, M. S. Hossain, X. Liu, et al., Unconventional chiral charge order in kagome superconductor KV3Sb5, Nat. Mater. 20, 1353 (2021).
  16. X. Zhou, Y. Li, X. Fan, J. Hao, Y. Dai, Z. Wang, Y. Yao, and H.-H. Wen, Origin of charge density wave in the kagome metal CsV3Sb5 as revealed by optical spectroscopy, Phys. Rev. B 104, L041101 (2021).
  17. K. Nakayama, Y. Li, T. Kato, M. Liu, Z. Wang, T. Takahashi, Y. Yao, and T. Sato, Multiple energy scales and anisotropic energy gap in the charge-density-wave phase of the kagome superconductor CsV3Sb5, Phys. Rev. B 104, L161112 (2021).
  18. Y. Luo, Y. Han, J. Liu, H. Chen, Z. Huang, L. Huai, H. Li, B. Wang, J. Shen, S. Ding, et al., A unique van Hove singularity in kagome superconductor CsV3−xTaxSb5 with enhanced superconductivity, Nat. Commun. 14, 3819 (2023).
  19. X. Teng, J. S. Oh, H. Tan, L. Chen, J. Huang, B. Gao, J.-X. Yin, J.-H. Chu, M. Hashimoto, D. Lu, C. Jozwiak, A. Bostwick, E. Rotenberg, G. E. Granroth, B. Yan, R. J. Birgeneau, P. Dai, and M. Yi, Magnetism and charge density wave order in kagome FeGe, Nat. Phys. 19, 814 (2023).
  20. A. Mielke, Ferromagnetic ground states for the Hubbard model on line graphs, J. Phys. A: Math. Gen. 24, L73 (1991); Ferromagnetism in the Hubbard model on line graphs and further considerations, 24, 3311 (1991); Exact ground states for the Hubbard model on the kagome lattice, J. Phys. A 25, 4335 (1992).
  21. H. Tasaki, Ferromagnetism in the Hubbard models with degenerate single-electron ground states, Phys. Rev. Lett. 69, 1608 (1992).
  22. A. Mielke and H. Tasaki, Ferromagnetism in the Hubbard model, Commun. Math. Phys. 158, 341 (1993).
  23. N. Regnault, Y. Xu, M.-R. Li, D.-S. Ma, M. Jovanovic, A. Yazdani, S. S. P. Parkin, C. Felser, L. M. Schoop, N. P. Ong, R. J. Cava, L. Elcoro, Z.-D. Song, and B. A. Bernevig, Catalogue of flat-band stoichiometric materials, Nature (London) 603, 824 (2022).
  24. D. Călugăru, A. Chew, L. Elcoro, Y. Xu, N. Regnault, Z.-D. Song, and B. A. Bernevig, General construction and topological classification of crystalline flat bands, Nat. Phys. 18, 185 (2022).
  25. Y. Cao, V. Fatemi, A. Demir, S. Fang, S. L. Tomarken, J. Y. Luo, J. D. Sanchez-Yamagishi, K. Watanabe, T. Taniguchi, E. Kaxiras, R. C. Ashoori, and P. Jarillo-Herrero, Correlated insulator behaviour at half-filling in magic-angle graphene superlattices, Nature (London) 556, 80 (2018).
  26. Y. Cao, V. Fatemi, S. Fang, K. Watanabe, T. Taniguchi, E. Kaxiras, and P. Jarillo-Herrero, Unconventional superconductivity in magic-angle graphene superlattices, Nature (London) 556, 43 (2018).
  27. M. I. B. Utama, R. J. Koch, K. Lee, N. Leconte, H. Li, S. Zhao, L. Jiang, J. Zhu, K. Watanabe, T. Taniguchi, P. D. Ashby, A. Weber-Bargioni, A. Zettl, C. Jozwiak, J. Jung, E. Rotenberg, A. Bostwick, and F. Wang, Visualization of the flat electronic band in twisted bilayer graphene near the magic angle twist, Nat. Phys. 17, 184 (2021).
  28. S. Lisi, X. Lu, T. Benschop, T. A. de Jong, P. Stepanov, J. R. Duran, F. Margot, I. Cucchi, E. Cappelli, A. Hunter, et al., Observation of flat bands in twisted bilayer graphene, Nat. Phys. 17, 189 (2021).
  29. Z. Lin, J.-H. Choi, Q. Zhang, W. Qin, S. Yi, P. Wang, L. Li, Y. Wang, H. Zhang, Z. Sun, L. Wei, S. Zhang, T. Guo, Q. Lu, J.-H. Cho, C. Zeng, and Z. Zhang, Flatbands and emergent ferromagnetic ordering in Fe3Sn2 kagome lattices, Phys. Rev. Lett. 121, 096401 (2018).
  30. M. Kang, L. Ye, S. Fang, J.-S. You, A. Levitan, M. Han, J. I. Facio, C. Jozwiak, A. Bostwick, E. Rotenberg, et al., Dirac fermions and flat bands in the ideal kagome metal FeSn, Nat. Mater. 19, 163 (2020).
  31. Z. Liu, M. Li, Qi Wang, G. Wang, C. Wen, K. Jiang, X. Lu, S. Yan, Y. Huang, D. Shen, J.-X. Yin, Z. Wang, Z. Yin, H. Lei, and S. Wang, Orbital-selective Dirac fermions and extremely flat bands in frustrated kagome-lattice metal CoSn, Nat. Commun. 11, 4002 (2020).
  32. A. L. Sharpe, E. J. Fox, A. W. Barnard, J. Finney, K. Watanabe, T. Taniguchi, M. A. Kastner, and D. Goldhaber-Gordon, Emergent ferromagnetism near three-quarters filling in twisted bilayer graphene, Science 365, 605 (2019).
  33. Y. Jiang, X. Lai, K. Watanabe, T. Taniguchi, K. Haule, J. Mao, and E. Y. Andrei, Charge order and broken rotational symmetry in magic-angle twisted bilayer graphene, Nature (London) 573, 91 (2019).
  34. Y. Cao, D. Chowdhury, D. Rodan-Legrain, O. Rubies-Bigorda, K. Watanabe, T. Taniguchi, T. Senthil, and P. Jarillo-Herrero, Strange metal in magic-angle graphene with near Planckian dissipation, Phys. Rev. Lett. 124, 076801 (2020).
  35. Y. Choi, H. Kim, Y. Peng, A. Thomson, C. Lewandowski, R. Polski, Y. Zhang, H. S. Arora, K. Watanabe, T. Taniguchi, J. Alicea, and S. Nadj-Perge, Correlation-driven topological phases in magic-angle twisted bilayer graphene, Nature (London) 589, 536 (2021).
  36. Y. Cao, D. Rodan-Legrain, J. M. Park, N. F. Q. Yuan, K. Watanabe, T. Taniguchi, R. M. Fernandes, L. Fu, and P. Jarillo-Herrero, Nematicity and competing orders in superconducting magic-angle graphene, Science 372, 264 (2021).
  37. S. Gao, S. Zhang, C. Wang, S. Yan, X. Han, X. Ji, W. Tao, J. Liu, T. Wang, S. Yuan, et al., Discovery of a single-band Mott insulator in a van der Waals flat-band compound, Phys. Rev. X 13, 041049 (2023).
  38. L. Ye, S. Fang, M. Kang, J. Kaufmann, Y. Lee, C. John, P. M. Neves, S. Y. Frank Zhao, J. Denlinger, C. Jozwiak, A. Bostwick, E. Rotenberg, E. Kaxiras, D. C. Bell, O. Janson, R. Comin, and J. G. Checkelsky, Hopping frustration-induced flat band and strange metallicity in a kagome metal, Nat. Phys. 20, 610 (2024).
  39. D. L. Bergman, C. Wu, and L. Balents, Band touching from real-space topology in frustrated hopping models, Phys. Rev. B 78, 125104 (2008).
  40. H.-M. Guo and M. Franz, Three-dimensional topological insulators on the pyrochlore lattice, Phys. Rev. Lett. 103, 206805 (2009).
  41. J. P. Wakefield, M. Kang, P. M. Neves, D. Oh, S. Fang, R. McTigue, S. Y. Frank Zhao, T. N. Lamichhane, A. Chen, S. Lee, et al., Three-dimensional flat bands in pyrochlore metal CaNi2, Nature (London) 623, 301 (2023).
  42. J. Huang, L. Chen, Y. Huang, C. Setty, B. Gao, Y. Shi, Z. Liu, Y. Zhang, T. Yilmaz, E. Vescovo, M. Hashimoto, D. Lu, B. I. Yakobson, P. Dai, J.-H. Chu, Q. Si, and M. Yi, Non-Fermi liquid behaviour in a correlated flat-band pyrochlore lattice, Nat. Phys. 20, 603 (2024).
  43. J. Huang, C. Setty, L. Deng, J.-Y. You, H. Liu, S. Shao, J. S. Oh, Y. Guo, Y. Zhang, Z. Yue, et al., Observation of flat bands and Dirac cones in a pyrochlore lattice superconductor, npj Quantum Mater, 9, 71 (2024).
  44. D. Pesin and L. Balents, Mott physics and band topology in materials with strong spin–orbit interaction, Nat. Phys. 6, 376 (2010).
  45. C. Weeks and M. Franz, Flat bands with nontrivial topology in three dimensions, Phys. Rev. B 85, 041104(R) (2012).
  46. J. Maciejko and G. A. Fiete, Fractionalized topological insulators, Nat. Phys. 11, 385 (2015).
  47. Y. Zhou, K.-H. Jin, H. Huang, Z. Wang, and F. Liu, Weyl points created by a three-dimensional flat band, Phys. Rev. B 99, 201105 ( R) (2019).
  48. Z. Y. Meng, F. Yang, K.-S. Chen, H. Yao, and H.-Y. Kee, Evidence for spin-triplet odd-parity superconductivity close to type-II van Hove singularities, Phys. Rev. B 91, 184509 (2015).
  49. H. Yao and F. Yang, Topological odd-parity superconductivity at type-II two-dimensional van Hove singularities, Phys. Rev. B 92, 035132 (2015).
  50. G. Kresse and J. Hafner, Ab initio molecular-dynamics simulation of the liquid-metal–amorphous-semiconductor transition in germanium, Phys. Rev. B 49, 14251 (1994).
  51. G. Kresse and J. Furthmüller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Phys. Rev. B 54, 11169 (1996).
  52. P. E. Blöchl, Projector augmented-wave method, Phys. Rev. B 50, 17953 (1994).
  53. J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996); 78, 1396(E) (1997).
  54. J. P. Perdew, K. Burke, and M. Ernzerhof, Perdew, Burke, and Ernzerhof reply, Phys. Rev. Lett. 80, 891 (1998).
  55. M. Ernzerhof and G. E. Scuseria, Assessment of the Perdew–Burke–Ernzerhof exchange-correlation functional, J. Chem. Phys. 110, 5029 (1999).
  56. 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).
  57. M. Kitamura, S. Souma, A. Honma, D. Wakabayashi, H. Tanaka, A. Toyoshima, K. Amemiya, T. Kawakami, K. Sugawara, K. Nakayama, K. Yoshimatsu, H. Kumigashira, T. Sato, and K. Horiba, Development of a versatile micro-focused angle-resolved photoemission spectroscopy system with Kirkpatrick–Baez mirror optics, Rev. Sci. Instrum. 93, 033906 (2022).
  58. S. S. Philip, S. Liu, J. C. Y. Teo, P. V. Balachandran, and D. Louca, Exploring the Dirac nature of RbBi2, Phys. Rev. B 107, 035143 (2023).
  59. S. Gutowska, B. Wiendlocha, T. Klimczuk, and M. Winiarski, Superconductivity in bismuth pyrochlore lattice compounds RbBi2 and CsBi2: The role of relativistic effects, J. Phys. Chem. C 127, 14402 (2023).
  60. S. Sun, K. Liu, and H. Lei, Type-I superconductivity in KBi2 single crystals, J. Phys.: Condens. Matter 28, 085701 (2016).
  61. S. S. Philip, J. Yang, D. Louca, P. F. S. Rosa, J. D. Thompson, and K. L. Page, Bismuth kagome sublattice distortions by quenching and flux pinning in superconducting RbBi2, Phys. Rev. B 104, 104503 (2021).
  62. H. Li, M. Ikeda, A. Suzuki, T. Taguchi, Y. Zhang, H. Goto, R. Eguchi, Y.-F. Liao, H. Ishii, and Y. Kubozono, Pressure dependence of superconductivity in alkali-Bi compounds KBi2 and RbBi2, Phys. Chem. Chem. Phys. 24, 7185 (2022).
  63. Z. Zhang, Z.-M. Yu, G.-B. Liu, and Y. Yao, MagneticTB: A package for tight-binding model of magnetic and non-magnetic materials, Comput. Phys. Commun. 270, 108153 (2022).
  64. D. Oh, J. Kang, Y. Qian, S. Fang, M. Kang, C. Jozwiak, A. Bostwick, E. Rotenberg, J. G. Checkelsky, L. Fu, T. Klimczuk, M. J. Winiarski, B.-J. Yang, and R. Comin, Nodal fermions in the strongly spin-orbit coupled pyrochlore-lattice compound RbBi2, Phys. Rev. B 110, 205102 (2024).
  65. L. Fu and C. L. Kane, Topological insulators with inversion symmetry, Phys. Rev. B 76, 045302 (2007).
  66. L. Fu, C. L. Kane, and E. J. Mele, Topological insulators in three dimensions, Phys. Rev. Lett. 98, 106803 (2007).
  67. L. Fu, Topological crystalline insulators, Phys. Rev. Lett. 106, 106802 (2011).
  68. W. Song, G. Liu, H. Deng, T. Yang, Y. Li, X.-Y. Yan, R. Liao, Q. Wang, J. Xu, C. Yan, et al., Many-body electronic structure in the pyrochlore superconductor CsBi2 and spin-liquid candidate Pr2Ir2O7, Phys. Rev. B 112, 245131 (2025).
  69. H.-Y. Li, H. Tan, H.-Y. Zhu, H.-K. Yuan, and M.-Q. Kuang, Directional criticality and higher-order flatness: Designing van Hove singularities in three dimensions, arXiv:2604.07806.
  70. Y. Zheng, L. Li, N. Luo, L.-M. Tang, Y. Feng, K.-Q. Chen, Z. Zhang, and J. Zeng, Orbital-designed flat-band model and realization of superconductivity in three-dimensional materials, Phys. Rev. B 109, L180504 (2024).
  71. K. Momma and F. Izumi, VESTA 3 for three-dimensional visualization of crystal, volumetric and morphology data, J. Appl. Cryst. 44, 1272 (2011).
  72. 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).
  73. 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. Sect. A: Found. Crystallogr. 62, 115 (2006).
  74. Z.-M. Yu, Z. Zhang, G.-B. Liu, W. Wu, X.-P. Li, R.-W. Zhang, S. A. Yang, and Y. Yao, Encyclopedia of emergent particles in three-dimensional crystals, Sci. Bull. 67, 375 (2022).
  75. L. Elcoro, B. Bradlyn, Z. Wang, M. G. Vergniory, J. Cano, C. Felser, B. A. Bernevig, D. Orobengoa, G. Flor, and M. I. Aroyo, Double crystallographic groups and their representations on the Bilbao Crystallographic Server, J. Appl. Cryst. 50, 1457 (2017).
  76. B. Bradlyn, L. Elcoro, J. Cano, M. G. Vergniory, Z. Wang, C. Felser, M. I. Aroyo, and B. A. Bernevig, Topological quantum chemistry, Nature (London) 547, 298 (2017).
  77. M. G. Vergniory, L. Elcoro, Z. Wang, J. Cano, C. Felser, M. I. Aroyo, B. A. Bernevig, and B. Bradlyn, Graph theory data for topological quantum chemistry, Phys. Rev. E 96, 023310 (2017).
  78. J. Cano, B. Bradlyn, Z. Wang, L. Elcoro, M. G. Vergniory, C. Felser, M. I. Aroyo, and B. A. Bernevig, Building blocks of topological quantum chemistry: Elementary band representations, Phys. Rev. B 97, 035139 (2018).
  79. H. C. Po, H. Watanabe, and A. Vishwanath, Fragile topology and Wannier obstructions, Phys. Rev. Lett. 121, 126402 (2018).
  80. D.-S. Ma, Y. Xu, C. S. Chiu, N. Regnault, A. A. Houck, Z. Song, and B. A. Bernevig, Spin-orbit-induced topological flat bands in line and split graphs of bipartite lattices, Phys. Rev. Lett. 125, 266403 (2020).
  81. K. Kuroki, T. Higashida, and R. Arita, High-Tc superconductivity due to coexisting wide and narrow bands: A fluctuation exchange study of the Hubbard ladder as a test case, Phys. Rev. B 72, 212509 (2005).
  82. K. Matsumoto, D. Ogura, and K. Kuroki, Wide applicability of high-Tc pairing originating from coexisting wide and incipient narrow bands in quasi-one-dimensional systems, Phys. Rev. B 97, 014516 (2018).
  83. H. Aoki, Theoretical possibilities for flat band superconductivity, J. Supercond. Nov. Magn. 33, 2341 (2020).

Outline

Information

Phys. Rev. Research 8, 033253– Published 3 September, 2026
  • Received 29 August 2024
  • Accepted 15 July 2026
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation