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Microscopic mechanism of high-temperature superconductivity revealed by ab initio studies on hole-doped multilayer cuprates HgBa2Ca2Cu3O8 under pressure

Ryui Kaneko1,* and Masatoshi Imada1,2,†

  • *Contact author: ryuikaneko@sophia.ac.jp
  • †Contact author: imada@g.ecc.u-tokyo.ac.jp
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Phys. Rev. Research 8, 043024 – Published 8 October, 2026

DOI: https://doi.org/10.1103/qqvw-ltth

Abstract

Triple-layer cuprate superconductor HgBa2Ca2Cu3O8 (Hg1223) keeps the record of the highest superconducting (SC) critical temperature Tc∼134K among all the existing materials at ambient pressure. Tc further increases under pressure up to Tc∼160K, thereby holding the key to the realistic and comprehensive understanding of the cuprate superconductors, which is one of the grand challenges in physics. However, the microscopic mechanism of high Tc of Hg1223 remains to be elucidated. Here, we perform first-principles calculations of Hg1223 both at ambient and applied pressures by solving ab initio Hamiltonians with an accurate variational solver supplemented by a neural network. The pressure dependence of the calculated d-wave SC order parameter and estimated Tc shows a structure supporting a Tc peak around 30 GPa in quantitative agreement with the reported experimental indications. The origin of the strong SC amplitude of Hg1223 at ambient pressure compared to other cuprates is identified as strong local Coulomb repulsion U attributed to poorer screening of the Coulomb interaction in multilayer compounds. The origin of the further increase in Tc under pressure is ascribed to a unique interplay of three elements, namely, increased electron hopping t, decreased U, and more importantly, strongly reduced nonlocal Coulomb repulsion V with increasing pressure. The origin of Cooper pairing is identified as the emergent local attraction counterintuitively arising from the strong bare local repulsion U for Hg1223. It explains why Hg1223 shows the highest Tc among other cuprates, while the pairing mechanism is common in other cuprates as well. The emergent attraction is interpreted from “attraction from reduced repulsion,” originating from the release of the fluctuating doubly occupied sites characterized from the “false vacuum” in the Mott insulator to the double-occupation-free d-wave SC states caused by the carrier doping. This instantaneous and local attraction is in marked contrast with the case of the conventional BCS SC mediated by bosonic glues. The local attraction is consistent with the electron fractionalization supported in experimental analyses. The coexistence of SC and antiferromagnetic orders is also demonstrated as a characteristic feature of the multilayer system with self-doping in the underdoped region. The quantitative and microscopic understanding of the high Tc in Hg1223 provides a new perspective on the origin of the cuprate superconductivity and offers a new route explicitly using this channel of the emergent attraction for future superconductivity research aiming at designing and optimizing SC materials.

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References (88)

  1. J. G. Bednorz and K. A. Möller, Possible high Tc superconductivity in the Ba-La-Cu-O system, Z. Phys. B 64, 189 (1986).
  2. M. T. Schmid, J.-B. Morée, R. Kaneko, Y. Yamaji, and M. Imada, Superconductivity studied by solving ab initio low-energy effective Hamiltonians for carrier doped CaCuO2, Bi2Sr2CuO6, Bi2Sr2CaCu2O8, and HgBa2CuO4, Phys. Rev. X 13, 041036 (2023).
  3. D. Tahara and M. Imada, Variational Monte Carlo method combined with quantum-number projection and multi-variable optimization, J. Phys. Soc. Jpn. 77, 114701 (2008).
  4. T. Misawa, S. Morita, K. Yoshimi, M. Kawamura, Y. Motoyama, K. Ido, T. Ohgoe, M. Imada, and T. Kato, mVMC—Open-source software for many-variable variational Monte Carlo method, Comput. Phys. Commun. 235, 447 (2019).
  5. Y. Nomura, A. S. Darmawan, Y. Yamaji, and M. Imada, Restricted Boltzmann machine learning for solving strongly correlated quantum systems, Phys. Rev. B 96, 205152 (2017).
  6. L. Finger, R. Hazen, R. Downs, R. Meng, and C. Chu, Crystal chemistry of HgBa2CaCu2O8+δ and HgBa2Ca2Cu3O8+δ single-crystal x-ray diffraction results, Physica C 226, 216 (1994).
  7. R. T. Downs, Topology of the pyroxenes as a function of temperature, pressure, and composition as determined from the procrystal electron density, Am. Mineral. 88, 556 (2003).
  8. S. Gražulis, D. Chateigner, R. T. Downs, A. F. T. Yokochi, M. Quirós, L. Lutterotti, E. Manakova, J. Butkus, P. Moeck, and A. Le Bail, Crystallography Open Database—An open-access collection of crystal structures, J. Appl. Crystallogr. 42, 726 (2009).
  9. A. Vaitkus, A. Merkys, T. Sander, M. Quirós, P. A. Thiessen, E. E. Bolton, and S. Gražulis, A workflow for deriving chemical entities from crystallographic data and its application to the crystallography open database, J. Cheminform. 15, 123 (2023).
  10. K. Momma and F. Izumi, VESTA3 for three-dimensional visualization of crystal, volumetric and morphology data, J. Appl. Crystallogr. 44, 1272 (2011).
  11. S. N. Putilin, E. V. Antipov, O. Chmaissem, and M. Marezio, Superconductivity at 94 K in HgBa2Cu04+δ, Nature (London) 362, 226 (1993).
  12. A. Schilling, M. Cantoni, J. Guo, and H. R. Ott, Superconductivity above 130 K in the Hg-Ba-Ca-Cu-O system, Nature (London) 363, 56 (1993).
  13. L. Gao, Y. Y. Xue, F. Chen, Q. Xiong, R. L. Meng, D. Ramirez, C. W. Chu, J. H. Eggert, and H. K. Mao, Superconductivity up to 164 K in HgBa2Cam−1CumO2m+2+δ (m = 1, 2, and 3) under quasihydrostatic pressures, Phys. Rev. B 50, 4260 (1994).
  14. P. Dai, B. C. Chakoumakos, G. F. Sun, K. Wong, Y. Xin, and D. F. Lu, Synthesis and neutron powder diffraction study of the superconductor HgBa2Ca2Cu3O8+δ by Tl substitution, Physica C 243, 201 (1995).
  15. A. Yamamoto, N. Takeshita, C. Terakura, and Y. Tokura, High pressure effects revisited for the cuprate superconductor family with highest critical temperature, Nat. Commun. 6, 8990 (2015).
  16. H. Mukuda, S. Shimizu, A. Iyo, and Y. Kitaoka, High-Tc superconductivity and antiferromagnetism in multilayered copper oxides—A new paradigm of superconducting mechanism, J. Phys. Soc. Jpn. 81, 011008 (2012).
  17. K. Kurokawa, S. Isono, Y. Kohama, S. Kunisada, S. Sakai, R. Sekine, M. Okubo, M. D. Watson, T. K. Kim, C. Cacho, S. Shin, T. Tohyama, K. Tokiwa, and T. Kondo, Unveiling phase diagram of the lightly doped high-Tc cuprate superconductors with disorder removed, Nat. Commun. 14, 4064 (2023).
  18. J. Bardeen, L. N. Cooper, and J. R. Schrieffer, Theory of superconductivity, Phys. Rev. 108, 1175 (1957).
  19. J.-B. Morée, Y. Yamaji, and M. Imada, Dome structure in pressure dependence of superconducting transition temperature for HgBa2Ca2Cu3O8: Studies by ab initio low-energy effective Hamiltonian, Phys. Rev. Res. 6, 023163 (2024).
  20. J.-B. Morée, M. Hirayama, M. T. Schmid, Y. Yamaji, and M. Imada, Ab initio low-energy effective Hamiltonians for the high-temperature superconducting cuprates Bi2Sr2CuO6,Bi2Sr2CaCu2O8,HgBa2CuO4, and CaCuO2, Phys. Rev. B 106, 235150 (2022).
  21. F. Aryasetiawan, J. M. Tomczak, T. Miyake, and R. Sakuma, Downfolded self-energy of many-electron systems, Phys. Rev. Lett. 102, 176402 (2009).
  22. M. Hirayama, T. Miyake, and M. Imada, Derivation of static low-energy effective models by an ab initio downfolding method without double counting of Coulomb correlations: Application to SrVO3, FeSe, and FeTe, Phys. Rev. B 87, 195144 (2013).
  23. M. Hirayama, T. Miyake, M. Imada, and S. Biermann, Low-energy effective Hamiltonians for correlated electron systems beyond density functional theory, Phys. Rev. B 96, 075102 (2017).
  24. F. Aryasetiawan, M. Imada, A. Georges, G. Kotliar, S. Biermann, and A. I. Lichtenstein, Frequency-dependent local interactions and low-energy effective models from electronic structure calculations, Phys. Rev. B 70, 195104 (2004).
  25. M. Imada and T. Miyake, Electronic structure calculation by first principles for strongly correlated electron systems, J. Phys. Soc. Jpn. 79, 112001 (2010).
  26. M. Hirayama, T. Misawa, T. Ohgoe, Y. Yamaji, and M. Imada, Effective Hamiltonian for cuprate superconductors derived from multiscale ab initio scheme with level renormalization, Phys. Rev. B 99, 245155 (2019).
  27. H. Yokoyama and H. Shiba, Variational Monte-Carlo studies of Hubbard model. I, J. Phys. Soc. Jpn. 56, 1490 (1987).
  28. C. Gros, R. Joynt, and T. M. Rice, Antiferromagnetic correlations in almost-localized Fermi liquids, Phys. Rev. B 36, 381 (1987).
  29. C. Gros, Superconductivity in correlated wave functions, Phys. Rev. B 38, 931 (1988).
  30. L. Capriotti, F. Becca, A. Parola, and S. Sorella, Resonating valence bond wave functions for strongly frustrated spin systems, Phys. Rev. Lett. 87, 097201 (2001).
  31. G. Carleo and M. Troyer, Solving the quantum many-body problem with artificial neural networks, Science 355, 602 (2017).
  32. Y. Nomura and M. Imada, Dirac-type nodal spin liquid revealed by refined quantum many-body solver using neural-network wave function, correlation ratio, and level spectroscopy, Phys. Rev. X 11, 031034 (2021).
  33. https://www.pasums.issp.u-tokyo.ac.jp/mvmc/en/about.
  34. M. C. Gutzwiller, Effect of correlation on the ferromagnetism of transition metals, Phys. Rev. Lett. 10, 159 (1963).
  35. R. Jastrow, Many-body problem with strong forces, Phys. Rev. 98, 1479 (1955).
  36. M. Capello, F. Becca, M. Fabrizio, S. Sorella, and E. Tosatti, Variational description of Mott insulators, Phys. Rev. Lett. 94, 026406 (2005).
  37. H. Yokoyama and H. Shiba, Variational Monte-Carlo studies of Hubbard model. III. Intersite correlation effects, J. Phys. Soc. Jpn. 59, 3669 (1990).
  38. J. Bouchaud, A. Georges, and C. Lhuillier, Pair wave functions for strongly correlated fermions and their determinantal representation, J. Phys. France 49, 553 (1988).
  39. M. Bajdich, L. Mitas, L. K. Wagner, and K. E. Schmidt, Pfaffian pairing and backflow wavefunctions for electronic structure quantum Monte Carlo methods, Phys. Rev. B 77, 115112 (2008).
  40. S. Sorella, Generalized Lanczos algorithm for variational quantum Monte Carlo, Phys. Rev. B 64, 024512 (2001).
  41. E. Heeb and T. Rice, Systematic improvement of variational Monte Carlo using Lanczos iterations, Z. Phys. B 90, 73 (1993).
  42. T. Misawa and M. Imada, Origin of high-Tc superconductivity in doped Hubbard models and their extensions: Roles of uniform charge fluctuations, Phys. Rev. B 90, 115137 (2014).
  43. K. Ido, K. Yoshimi, T. Misawa, and M. Imada, Unconventional dual 1D–2D quantum spin liquid revealed by ab initio studies on organic solids family, npj Quantum Mater. 7, 48 (2022).
  44. M. Imada and T. Kashima, Path-integral renormalization group method for numerical study of strongly correlated electron systems, J. Phys. Soc. Jpn. 69, 2723 (2000).
  45. T. Kashima and M. Imada, Path-integral renormalization group method for numerical study on ground states of strongly correlated electron systems, J. Phys. Soc. Jpn. 70, 2287 (2001).
  46. D. Wu, R. Rossi, F. Vicentini, N. Astrakhantsev, F. Becca, X. Cao, J. Carrasquilla, F. Ferrari, A. Georges, M. Hibat-Allah, et al., Variational benchmarks for quantum many-body problems, Science 386, 296 (2024).
  47. J. Tranquada, B. Sternlieb, J. Axe, Y. Nakamura, and S.-I. Uchida, Evidence for stripe correlations of spins and holes in copper oxide superconductors, Nature (London) 375, 561 (1995).
  48. J. M. Tranquada, J. D. Axe, N. Ichikawa, A. R. Moodenbaugh, Y. Nakamura, and S. Uchida, Coexistence of, and competition between, superconductivity and charge-stripe order in La1.6−xNd0.4SrxCuO4, Phys. Rev. Lett. 78, 338 (1997).
  49. Y. Iqbal, F. Becca, S. Sorella, and D. Poilblanc, Gapless spin-liquid phase in the kagome spin-12 Heisenberg antiferromagnet, Phys. Rev. B 87, 060405 (2013).
  50. H.-H. Zhao, K. Ido, S. Morita, and M. Imada, Variational Monte Carlo method for fermionic models combined with tensor networks and applications to the hole-doped two-dimensional Hubbard model, Phys. Rev. B 96, 085103 (2017).
  51. K. Ido, T. Ohgoe, and M. Imada, Competition among various charge-inhomogeneous states and d-wave superconducting state in Hubbard models on square lattices, Phys. Rev. B 97, 045138 (2018).
  52. T. Ohgoe, M. Hirayama, T. Misawa, K. Ido, Y. Yamaji, and M. Imada, Ab initio study of superconductivity and inhomogeneity in a Hg-based cuprate superconductor, Phys. Rev. B 101, 045124 (2020).
  53. A. Fukuoka, A. Tokiwa-Yamamoto, M. Itoh, R. Usami, S. Adachi, and K. Tanabe, Dependence of Tc and transport properties on the Cu valence in HgBa2Can−1CunO2(n+1)+δ (n = 2,3) superconductors, Phys. Rev. B 55, 6612 (1997).
  54. H. Kotegawa, Y. Tokunaga, K. Ishida, G.-Q. Zheng, Y. Kitaoka, H. Kito, A. Iyo, K. Tokiwa, T. Watanabe, and H. Ihara, Unusual magnetic and superconducting characteristics in multilayered high-Tc cuprates: Cu63 NMR study, Phys. Rev. B 64, 064515 (2001).
  55. S.-I. Ideta, S. Adachi, T. Noji, S. Yamaguchi, N. Sasaki, S. Ishida, S.-I. Uchida, T. Fujii, T. Watanabe, W. O. Wang, B. Moritz, T. P. Devereaux, M. Arita, C.-Y. Mou, T. Yoshida, K. Tanaka, T.-K. Lee, and A. Fujimori, Proximity-induced nodal metal in an extremely underdoped CuO2 plane in triple-layer cuprates, Nat. Commun. 16, 9470 (2025).
  56. K. Nakamura, Y. Yoshimoto, and M. Imada, Ab initio two-dimensional multiband low-energy models of EtMe3Sb[Pd(dmit)2]2 and κ−(BEDT−TTF)2Cu(NCS)2 with comparisons to single-band models, Phys. Rev. B 86, 205117 (2012).
  57. D. T. Jover, R. J. Wijngaarden, H. Wilhelm, R. Griessen, S. M. Loureiro, J.-J. Capponi, A. Schilling, and H. R. Ott, Pressure dependence of the superconducting critical temperature of HgBa2Ca2Cu3O8+y and HgBa2Ca3Cu4O10+y up to 30 GPa, Phys. Rev. B 54, 4265 (1996).
  58. J. W. Alldredge, J. Lee, K. McElroy, M. Wang, K. Fujita, Y. Kohsaka, C. Taylor, H. Eisaki, S. Uchida, P. J. Hirschfeld, and J. C. Davis, Evolution of the electronic excitation spectrum with strongly diminishing hole density in superconducting Bi2Sr2CaCu2O8+δ, Nat. Phys. 4, 319 (2008).
  59. S. Sakai, M. Civelli, and M. Imada, Direct connection between Mott insulators and d-wave high-temperature superconductors revealed by continuous evolution of self-energy poles, Phys. Rev. B 98, 195109 (2018).
  60. D. J. Scalapino, E. Loh, and J. E. Hirsch, d-wave pairing near a spin-density-wave instability, Phys. Rev. B 34, 8190(R) (1986).
  61. Y. Ohta, T. Tohyama, and S. Maekawa, Apex oxygen and critical temperature in copper oxide superconductors: Universal correlation with the stability of local singlets, Phys. Rev. B 43, 2968 (1991).
  62. M. R. Koblischka, S. Roth, A. Koblischka-Veneva, T. Karwoth, A. Wiederhold, X. L. Zeng, S. Fasoulas, and M. Murakami, Relation between crystal structure and transition temperature of superconducting metals and alloys, Metals 10, 158 (2020).
  63. Z. Al-Ruqaishi and C. R. Ooi, Multi-variable empirical equation for critical temperature of cuprate superconductors, Results Phys. 81, 108576 (2026).
  64. J. Attfield, A. Kharlanov, and J. McAllister, Cation effects in doped La2CuO4 superconductors, Nature (London) 394, 157 (1998).
  65. H. Hobou, S. Ishida, K. Fujita, M. Ishikado, K. M. Kojima, H. Eisaki, and S. Uchida, Enhancement of the superconducting critical temperature in Bi2Sr2CaCu2O8+δ by controlling disorder outside CuO2 planes, Phys. Rev. B 79, 064507 (2009).
  66. F. Nilsson, K. Karlsson, and F. Aryasetiawan, Dynamically screened Coulomb interaction in the parent compounds of hole-doped cuprates: Trends and exceptions, Phys. Rev. B 99, 075135 (2019).
  67. M. Kitatani, L. Si, P. Worm, J. M. Tomczak, R. Arita, and K. Held, Optimizing superconductivity: From cuprates via nickelates to palladates, Phys. Rev. Lett. 130, 166002 (2023).
  68. J.-B. Morée and R. Arita, Universal chemical formula dependence of ab initio low-energy effective Hamiltonian in single-layer carrier-doped cuprate superconductors: Study using a hierarchical dependence extraction algorithm, Phys. Rev. B 110, 014502 (2024).
  69. Y. J. Uemura, L. P. Le, G. M. Luke, B. J. Sternlieb, W. D. Wu, J. H. Brewer, T. M. Riseman, C. L. Seaman, M. B. Maple, M. Ishikawa, D. G. Hinks, J. D. Jorgensen, G. Saito, and H. Yamochi, Basic similarities among cuprate, bismuthate, organic, Chevrel-phase, and heavy-fermion superconductors shown by penetration-depth measurements, Phys. Rev. Lett. 66, 2665 (1991).
  70. N. Prokof’ev, O. Ruebenacker, and B. Svistunov, Critical point of a weakly interacting two-dimensional Bose gas, Phys. Rev. Lett. 87, 270402 (2001).
  71. Y. J. Uemura, G. M. Luke, B. J. Sternlieb, J. H. Brewer, J. F. Carolan, W. N. Hardy, R. Kadono, J. R. Kempton, R. F. Kiefl, S. R. Kreitzman, et al., Universal correlations between Tc and nsm* (carrier density over effective mass) in high-Tc cuprate superconductors, Phys. Rev. Lett. 62, 2317 (1989).
  72. X. Luo, H. Chen, Y. Li, Q. Gao, C. Yin, H. Yan, T. Miao, H. Luo, Y. Shu, Y. Chen, et al., Electronic origin of high superconducting critical temperature in trilayer cuprates, Nat. Phys. 19, 1841 (2023).
  73. X. Liu and M. Jiang, Enhanced superconductivity via layer differentiation in the trilayer Hubbard model, Phys. Rev. B 112, L201103 (2025).
  74. B. Bacq-Labreuil, B. Lacasse, A.-M. S. Tremblay, D. Sénéchal, and K. Haule, Toward an ab initio theory of high-temperature superconductors: A study of multilayer cuprates, Phys. Rev. X 15, 021071 (2025).
  75. Z.-H. Cui, J. Yang, J. Tölle, H.-Z. Ye, S. Yuan, H. Zhai, G. Park, R. Kim, X. Zhang, L. Lin, T. C. Berkelbach, and G. K.-L. Chan, Ab initio quantum many-body description of superconducting trends in the cuprates, Nat. Commun. 16, 1845 (2025).
  76. M. Imada and T. J. Suzuki, Excitons and dark fermions as origins of Mott gap, pseudogap and superconductivity in cuprate superconductors—General concept and basic formalism based on gap physics, J. Phys. Soc. Jpn. 88, 024701 (2019).
  77. S. Sakai, M. Civelli, and M. Imada, Hidden fermionic excitation boosting high-temperature superconductivity in cuprates, Phys. Rev. Lett. 116, 057003 (2016).
  78. S. Sakai, S. Blanc, M. Civelli, Y. Gallais, M. Cazayous, M.-A. Méasson, J. S. Wen, Z. J. Xu, G. D. Gu, G. Sangiovanni, Y. Motome, K. Held, A. Sacuto, A. Georges, and M. Imada, Raman-scattering measurements and theory of the energy-momentum spectrum for underdoped Bi2Sr2CaCuO8+δ superconductors: Evidence of an s-wave structure for the pseudogap, Phys. Rev. Lett. 111, 107001 (2013).
  79. M. Imada, Charge order and superconductivity as competing brothers in cuprate high-Tc superconductors, J. Phys. Soc. Jpn. 90, 111009 (2021).
  80. Y. Yamaji, T. Yoshida, A. Fujimori, and M. Imada, Hidden self-energies as origin of cuprate superconductivity revealed by machine learning, Phys. Rev. Res. 3, 043099 (2021).
  81. A. Singh, H. Y. Huang, J. D. Xie, J. Okamoto, C. T. Chen, T. Watanabe, A. Fujimori, M. Imada, and D. J. Huang, Unconventional exciton evolution from the pseudogap to superconducting phases in cuprates, Nat. Commun. 13, 7906 (2022).
  82. S. Sakai, Y. Yamaji, F. Imoto, T. Tamegai, A. Kaminski, T. Kondo, Y. Kohsaka, T. Hanaguri, and M. Imada, Unified description of cuprate superconductors by fractionalized electrons emerging from integrated analyses of photoemission spectra and quasiparticle interference, Phys. Rev. X 16, 011018 (2026).
  83. Y. Kamihara, T. Watanabe, M. Hirano, and H. Hosono, Iron-based layered superconductor La[O1−xFx]FeAs (x = 0.05–0.12) with Tc = 26 K, J. Am. Chem. Soc. 130, 3296 (2008).
  84. 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).
  85. H. Sun, M. Huo, X. Hu, J. Li, Z. Liu, Y. Han, L. Tang, Z. Mao, P. Yang, B. Wang, J. Cheng, D.-X. Yao, G.-M. Zhang, and M. Wang, Signatures of superconductivity near 80 K in a nickelate under high pressure, Nature (London) 621, 493 (2023).
  86. X.-J. Chen, V. V. Struzhkin, Y. Yu, A. F. Goncharov, C.-T. Lin, H.-K. Mao, and R. J. Hemley, Enhancement of superconductivity by pressure-driven competition in electronic order, Nature (London) 466, 950 (2010).
  87. J.-B. Morée (unpublished).
  88. H. Yokoyama, M. Ogata, Y. Tanaka, K. Kobayashi, and H. Tsuchiura, Crossover between BCS superconductor and doped Mott insulator of d-wave pairing state in two-dimensional Hubbard model, J. Phys. Soc. Jpn. 82, 014707 (2013).

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Phys. Rev. Research 8, 043024– Published 8 October, 2026
  • Received 25 March 2026
  • Accepted 16 September 2026
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