Theory of dual fermion superconductivity in hole-doped cuprates

  • Jun Chang
  • Jize Zhao
Regular Article


Since the discovery of the cuprate high-temperature superconductivity in 1986, a universal phase diagram has been constructed experimentally and numerous theoretical models have been proposed. However, there remains no consensus on the underlying physics thus far. Here, we theoretically investigate the phase diagram of hole-doped cuprates based on an itinerant-localized dual fermion model, with the charge carriers doped on the oxygen sites and localized holes on the copper dx2 − y2 orbitals. We analytically demonstrate that the puzzling anomalous normal state or the strange metal could simply stem from a free Fermi gas of carriers bathing in copper antiferromagnetic spin fluctuations. The short-range high-energy spin excitations also act as the “magnetic glue” of carrier Cooper pairs and induce d-wave superconductivity from the underdoped to overdoped regime, distinctly different from the conventional low-frequency magnetic fluctuation mechanism. We further sketch out the characteristic dome-shaped critical temperature Tc versus doping level. The emergence of the pseudogap is ascribed to the localization of partial carriers coupled to the local copper moments or a crossover from the strange metal to a nodal Kondo-like insulator. Our work provides a consistent theoretical framework to understand the typical phase diagram of hole-doped cuprates and paves a distinct way to the studies of both non-Fermi liquid and unconventional superconductivity in strongly correlated systems.


Solid State and Materials 


  1. 1.
    J. Bardeen, L.N. Cooper, J.R. Schrieffer, Phys. Rev. 108, 1175 (1957)ADSMathSciNetCrossRefGoogle Scholar
  2. 2.
    J.G. Bednorz, K.A. Müller, Z. Phys. B 64, 189 (1986)ADSCrossRefGoogle Scholar
  3. 3.
    Y. Kamihara, T. Watanabe, M. Hirano, H. Hosono, J. Am. Chem. Soc. 130, 3296 (2008)CrossRefGoogle Scholar
  4. 4.
    F. Steglich, J. Aarts, C.D. Bredl, W. Lieke, D. Meschede, W. Franz, H. Schäfer, Phys. Rev. Lett. 43, 1892 (1979)ADSCrossRefGoogle Scholar
  5. 5.
    M. Gurvitch, A. T. Fiory, Phys. Rev. Lett. 59, 1337 (1987)ADSCrossRefGoogle Scholar
  6. 6.
    G.A. Thomas, J. Orenstein, D.H. Rapkine, M. Capizzi, A.J. Millis, R.N. Bhatt, L.F. Schneemeyer, J.V. Waszczak, Phys. Rev. Lett. 61, 1313 (1988)ADSCrossRefGoogle Scholar
  7. 7.
    C.L. Seaman, M.B. Maple, B.W. Lee, S. Ghamaty, M.S. Torikachvili, J.-S. Kang, L.Z. Liu, J.W. Allen, D.L. Cox, Phys. Rev. Lett. 67, 2882 (1991)ADSCrossRefGoogle Scholar
  8. 8.
    E. Dagotto, Rev. Mod. Phys. 66, 763 (1994)ADSCrossRefGoogle Scholar
  9. 9.
    G.R. Stewart, Rev. Mod. Phys. 73, 797 (2001)ADSCrossRefGoogle Scholar
  10. 10.
    G.R. Stewart, Rev. Mod. Phys. 78, 743 (2006)ADSCrossRefGoogle Scholar
  11. 11.
    P.A. Lee, N. Nagaosa, X.-G. Wen, Rev. Mod. Phys. 78, 17 (2006)ADSCrossRefGoogle Scholar
  12. 12.
    D.J. Scalapino, Rev. Mod. Phys. 84, 1383 (2012)ADSCrossRefGoogle Scholar
  13. 13.
    B. Keimer, S.A. Kivelson, M.R. Norman, S. Uchida, J. Zaanen, Nature 518, 179 (2015)ADSCrossRefGoogle Scholar
  14. 14.
    C. Pfleiderer, Rev. Mod. Phys. 81, 1551 (2009)ADSCrossRefGoogle Scholar
  15. 15.
    T. Dahm, V. Hinkov, S.V. Borisenko, A.A. Kordyuk, V.B. Zabolotnyy, J. Fink, B. Buechner, D.J. Scalapino, W. Hanke, B. Keimer, Nat. Phys. 5, 217 (2009)CrossRefGoogle Scholar
  16. 16.
    J. P. Carbotte, T. Timusk, J. Hwang, Rep. Prog. Phys. 74, 066501 (2011)ADSCrossRefGoogle Scholar
  17. 17.
    D.J. Scalapino, E. Loh, J.E. Hirsch, Phys. Rev. B 34, 8190 (1986)ADSCrossRefGoogle Scholar
  18. 18.
    P. Monthoux, A.V. Balatsky, D. Pines, Phys. Rev. Lett. 67, 3448 (1991)ADSCrossRefGoogle Scholar
  19. 19.
    P. Monthoux, D. Pines, Phys. Rev. Lett. 69, 961 (1992)ADSCrossRefGoogle Scholar
  20. 20.
    T. Moriya, Y. Takahashi, K. Ueda, J. Phys. Soc. Jpn 59, 2905 (1990)ADSCrossRefGoogle Scholar
  21. 21.
    A.J. Millis, H. Monien, D. Pines, Phys. Rev. B 42, 167 (1990)ADSCrossRefGoogle Scholar
  22. 22.
    A. Chubukov, D. Pines, J. Schmalian, in Superconductivity, edited by K. Bennemann, J. Ketterson (Springer, Berlin, Heidelberg, 2008), pp. 1349–1413Google Scholar
  23. 23.
    T. Park, M.J. Graf, L. Boulaevskii, J.L. Sarrao, J.D. Thompson, Proc. Natl. Acad. Sci. USA 105, 6825 (2008)ADSCrossRefGoogle Scholar
  24. 24.
    P. McHale, P. Fulde, P. Thalmeier, Phys. Rev. B 70, 014513 (2004)ADSCrossRefGoogle Scholar
  25. 25.
    J. Chang, I. Eremin, P. Thalmeier, P. Fulde, Phys. Rev. B 75, 024503 (2007)ADSCrossRefGoogle Scholar
  26. 26.
    D. Rybicki, M. Jurkutat, S. Reichardt, C. Kapusta, J. Haase, Nat. Commun. 7, 11413 (2016)ADSCrossRefGoogle Scholar
  27. 27.
    J. Haase, C.P. Slichter, G.V.M. Williams, J. Phys.: Condens. Matter 21, 455702 (2009)ADSGoogle Scholar
  28. 28.
    K.A. Müller, J. Phys.: Condens. Matter 19, 251002 (2007)ADSGoogle Scholar
  29. 29.
    R.E. Walstedt, B.S. Shastry, S.-W. Cheong, Phys. Rev. Lett. 72, 3610 (1994)ADSCrossRefGoogle Scholar
  30. 30.
    N.J. Curro, T. Imai, C.P. Slichter, B. Dabrowski, Phys. Rev. B 56, 877 (1997)ADSCrossRefGoogle Scholar
  31. 31.
    Y. Li, G. Yu, M. K. Chan, V. Balédent, Y. Li, N. Barišić, X. Zhao, K. Hradil, R.A. Mole, Y. Sidis et al., Nat. Phys. 8, 404 (2012)CrossRefGoogle Scholar
  32. 32.
    V. Barzykin, D. Pines, Adv. Phys. 58, 1 (2009)ADSCrossRefGoogle Scholar
  33. 33.
    V.J. Emery, Phys. Rev. Lett. 58, 2794 (1987)ADSCrossRefGoogle Scholar
  34. 34.
    J. Zaanen, A.M. Oleś, Phys. Rev. B 37, 9423 (1988)ADSCrossRefGoogle Scholar
  35. 35.
    F.C. Zhang, T.M. Rice, Phys. Rev. B 37, 3759 (1988)ADSCrossRefGoogle Scholar
  36. 36.
    C.M. Varma, P.B. Littlewood, S. Schmitt-Rink, E. Abrahams, A.E. Ruckenstein, Phys. Rev. Lett. 63, 1996 (1989)ADSCrossRefGoogle Scholar
  37. 37.
    G. Aeppli, Z. Fisk, Comments Condens. Mater. Phys. 16, 155 (1992)Google Scholar
  38. 38.
    P. Coleman, in Handbook of Magnetism and Advanced Magnetic Materials, edited by H. Kronmüller, S. Parkin (John Wiley & Sons, New York, 2007), Vol. 1, pp. 95–148Google Scholar
  39. 39.
    P.W. Anderson, Science 235, 1196 (1987)ADSCrossRefGoogle Scholar
  40. 40.
    D.A. Wollman, D.J. Van Harlingen, W.C. Lee, D.M. Ginsberg, A.J. Leggett, Phys. Rev. Lett. 71, 2134 (1993)ADSCrossRefGoogle Scholar
  41. 41.
    C.C. Tsuei, J.R. Kirtley, Rev. Mod. Phys. 72, 969 (2000)ADSCrossRefGoogle Scholar
  42. 42.
    P.W. Anderson, Nat. Phys. 2, 626 (2006)CrossRefGoogle Scholar
  43. 43.
    J.M. Tranquada, P.M. Gehring, G. Shirane, S. Shamoto, M. Sato, Phys. Rev. B 46, 5561 (1992)ADSCrossRefGoogle Scholar
  44. 44.
    S.M. Hayden, H.A. Mook, P. Dai, T.G. Perring, F. Dogan, Nature 429, 531 (2004)ADSCrossRefGoogle Scholar
  45. 45.
    J.M. Tranquada, H. Woo, T.G. Perring, H. Goka, G.D. Gu, G. Xu, M. Fujita, K. Yamada, Nature 429, 534 (2004)ADSCrossRefGoogle Scholar
  46. 46.
    V. Hinkov, P. Bourges, S. Pailhes, Y. Sidis, A. Ivanov, C.D. Frost, T.G. Perring, C.T. Lin, D.P. Chen, B. Keimer, Nat. Phys. 3, 780 (2007)CrossRefGoogle Scholar
  47. 47.
    B. Vignolle, S.M. Hayden, D.F. McMorrow, H.M. Ronnow, B. Lake, C.D. Frost, T.G. Perring, Nat. Phys. 3, 163 (2007)CrossRefGoogle Scholar
  48. 48.
    O.J. Lipscombe, S.M. Hayden, B. Vignolle, D.F. McMorrow, T.G. Perring, Phys. Rev. Lett. 99, 067002 (2007)ADSCrossRefGoogle Scholar
  49. 49.
    B. Fauqué, Y. Sidis, L. Capogna, A. Ivanov, K. Hradil, C. Ulrich, A.I. Rykov, B. Keimer, P. Bourges, Phys. Rev. B 76, 214512 (2007)ADSCrossRefGoogle Scholar
  50. 50.
    M. Le Tacon, G. Ghiringhelli, J. Chaloupka, M.M. Sala, V. Hinkov, M.W. Haverkort, M. Minola, M. Bakr, K.J. Zhou, S. Blanco-Canosa et al., Nat. Phys. 7, 725 (2011)CrossRefGoogle Scholar
  51. 51.
    M.P.M. Dean, G. Dellea, R.S. Springell, F. Yakhou-Harris, K. Kummer, N.B. Brookes, X. Liu, Y.J. Sun, J. Strle, T. Schmitt et al., Nat. Mater. 12, 1019 (2013)ADSCrossRefGoogle Scholar
  52. 52.
    S.M. Hayden, G. Aeppli, H. Mook, D. Rytz, M.F. Hundley, Z. Fisk, Phys. Rev. Lett. 66, 821 (1991)ADSCrossRefGoogle Scholar
  53. 53.
    B. Keimer, R.J. Birgeneau, A. Cassanho, Y. Endoh, R.W. Erwin, M.A. Kastner, G. Shirane, Phys. Rev. Lett. 67, 1930 (1991)ADSCrossRefGoogle Scholar
  54. 54.
    M.R. Norman, A.V. Chubukov, Phys. Rev. B 73, 140501 (2006)ADSCrossRefGoogle Scholar
  55. 55.
    M. Takigawa, A.P. Reyes, P.C. Hammel, J.D. Thompson, R.H. Heffner, Z. Fisk, K.C. Ott, Phys. Rev. B 43, 247 (1991)ADSCrossRefGoogle Scholar
  56. 56.
    W.W. Warren, R.E. Walstedt, G.F. Brennert, R.J. Cava, R. Tycko, R.F. Bell, G. Dabbagh, Phys. Rev. Lett. 62, 1193 (1989)ADSCrossRefGoogle Scholar
  57. 57.
    H. Alloul, T. Ohno, P. Mendels, Phys. Rev. Lett. 63, 1700 (1989)ADSCrossRefGoogle Scholar
  58. 58.
    M.R. Norman, D. Pines, C. Kallin, Adv. Phys. 54, 715 (2005)ADSCrossRefGoogle Scholar
  59. 59.
    I.M. Vishik, M. Hashimoto, R.-H. He, W.-S. Leeb, F. Schmitt, D. Lu, R.G. Moore, C. Zhang, W. Meevasana, T. Sasagawa et al., Proc. Natl. Acad. Sci. USA 109, 18332 (2012)ADSCrossRefGoogle Scholar
  60. 60.
    A.V. Puchkov, D.N. Basov, T. Timusk, J. Phys.: Condens. Matter 8, 10049 (1996)ADSGoogle Scholar
  61. 61.
    C.C. Homes, T. Timusk, R. Liang, D.A. Bonn, W.N. Hardy, Phys. Rev. Lett. 71, 1645 (1993)ADSCrossRefGoogle Scholar
  62. 62.
    N. Doiron-Leyraud, S. Lepault, O. Cyr-Choinière, B. Vignolle, G. Grissonnanche, F. Laliberté, J. Chang, N. Barišić, M.K. Chan, L. Ji et al., Phys. Rev. X 3, 021019 (2013)Google Scholar
  63. 63.
    S. Badoux, S.A.A. Afshar, B. Michon, A. Ouellet, S. Fortier, D. LeBoeuf, T.P. Croft, C. Lester, S.M. Hayden, H. Takagi et al., Phys. Rev. X 6, 021004 (2016)Google Scholar
  64. 64.
    Y. Wang, C. Chubukov, Phys. Rev. B 90, 035149 (2014)ADSCrossRefGoogle Scholar
  65. 65.
    N. Bickers, D. Scalapino, R. Scalettar, Int. J. Mod. Phys. B 01, 687 (1987)ADSCrossRefGoogle Scholar
  66. 66.
    M. Inui, S. Doniach, P.J. Hirschfeld, A.E. Ruckenstein, Phys. Rev. B 37, 2320 (1988)ADSCrossRefGoogle Scholar
  67. 67.
    C. Dong, J.K. Liang, G.C. Che, S.S. Xie, Z.X. Zhao, Q.S. Yang, Y.M. Ni, G.R. Liu, Phys. Rev. B 37, 5182 (1988)ADSCrossRefGoogle Scholar
  68. 68.
    G. Kotliar, J. Liu, Phys. Rev. B 38, 5142 (1988)ADSCrossRefGoogle Scholar
  69. 69.
    H. Matsui, T. Sato, T. Takahashi, S.-C. Wang, H.-B. Yang, H. Ding, T. Fujii, T. Watanabe, A. Matsuda, Phys. Rev. Lett. 90, 217002 (2003)ADSCrossRefGoogle Scholar
  70. 70.
    E.E.M. Chia, D. Springer, S.K. Nair, X.Q. Zou, S.A. Cheong, C. Panagopoulos, T. Tamegai, H. Eisaki, S. Ishida, S. Uchida et al., New J. Phys. 15, 103027 (2013)ADSCrossRefGoogle Scholar
  71. 71.
    A.J. Millis, S. Sachdev, C.M. Varma, Phys. Rev. B 37, 4975 (1988)ADSCrossRefGoogle Scholar
  72. 72.
    P. W. Anderson, Science 316, 1705 (2007)CrossRefGoogle Scholar
  73. 73.
    P. Monthoux, D.J. Scalapino, Phys. Rev. B 50, 10339 (1994)ADSCrossRefGoogle Scholar
  74. 74.
    R.M. Martin, Phys. Rev. Lett. 48, 362 (1982)ADSCrossRefGoogle Scholar
  75. 75.
    M. Oshikawa, Phys. Rev. Lett. 84, 3370 (2000)ADSCrossRefGoogle Scholar
  76. 76.
    M. Norman, H. Ding, M. Randeria, J. Campuzano, T. Yokoya, T. Takeuchi, T. Takahashi, T. Mochiku, K. Kadowaki, P. Guptasarma et al., Nature 392, 157 (1998)ADSCrossRefGoogle Scholar
  77. 77.
    M.E. Simon, C.M. Varma, Phys. Rev. Lett. 89, 247003 (2002)ADSCrossRefGoogle Scholar
  78. 78.
    M. Ogata, H. Shiba, J. Phys. Soc. Jpn 57, 3074 (1988)ADSCrossRefGoogle Scholar
  79. 79.
    J.L. Shen, C.S. Ting, Phys. Rev. B 41, 1969 (1990)ADSCrossRefGoogle Scholar
  80. 80.
    A.V. Chubukov, D.L. Maslov, Phys. Rev. B 86, 155136 (2012)ADSCrossRefGoogle Scholar
  81. 81.
    S. Sakai, S. Blanc, M. Civelli, Y. Gallais, M. Cazayous, M.-A. Méasson, J.S. Wen, Z.J. Xu, G.D. Gu, G. Sangiovanni et al., Phys. Rev. Lett. 111, 107001 (2013)ADSCrossRefGoogle Scholar
  82. 82.
    Y. Li, M. Le Tacon, Y. Matiks, A.V. Boris, T. Loew, C.T. Lin, L. Chen, M.K. Chan, C. Dorow, L. Ji et al., Phys. Rev. Lett. 111, 187001 (2013)ADSCrossRefGoogle Scholar
  83. 83.
    C.C. Homes, S.V. Dordevic, M. Strongin, D.A. Bonn, R. Liang, W.N. Hardy, S. Komiya, Y. Ando, G. Yu, N. Kaneko et al., Nature 430, 539 (2004)ADSCrossRefGoogle Scholar
  84. 84.
    V.G. Kogan, Phys. Rev. B 87, 220507 (2013)ADSCrossRefGoogle Scholar
  85. 85.
    G. Rickayzen, in Superconductivity, edited by R.D. Parks (Dekker, New York, 1969), Vol. 1, p. 51Google Scholar
  86. 86.
    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., Phys. Rev. Lett. 62, 2317 (1989)ADSCrossRefGoogle Scholar
  87. 87.
    V.J. Emery, S.A. Kivelson, Nature 374, 434 (1995)ADSCrossRefGoogle Scholar
  88. 88.
    D. Valentinis, D. van der Marel, C. Berthod, Phys. Rev. B 94, 024511 (2016)ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  • Jun Chang
    • 1
    • 2
  • Jize Zhao
    • 3
  1. 1.College of Physics and Information Technology, Shaanxi Normal UniversityXi’anP.R. China
  2. 2.Institute of Theoretical PhysicsBeijingP.R. China
  3. 3.Institute of Applied Physics and Computational MathematicsBeijingP.R. China

Personalised recommendations