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A Theory for the High-T c Cuprates: Anomalous Normal-State and Spectroscopic Properties, Phase Diagram, and Pairing

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Abstract

A theory of highly correlated layered superconducting materials is applied for the cuprates. Differently from an independent-electron approximation, their low-energy excitations are approached in terms of auxiliary particles representing combinations of atomic-like electron configurations, where the introduction of a Lagrange Bose field enables treating them as bosons or fermions. The energy spectrum of this field accounts for the tendency of hole-doped cuprates to form stripe-like inhomogeneities. Consequently, it induces a different analytical behavior for auxiliary particles corresponding to “antinodal” and “nodal” electrons, enabling the existence of different pairing temperatures at T ∗ and T c . This theory correctly describes the observed phase diagram of the cuprates, including the non-Fermi-liquid to FL crossover in the normal state, the existence of Fermi arcs below T ∗ and of a “marginal-FL” critical behavior above it. The qualitative anomalous behavior of numerous physical quantities is accounted for, including kink- and waterfall-like spectral features, the drop in the scattering rates below T ∗ and more radically below T c , and an effective increase in the density of carriers with T and ω, reflected in transport, optical and other properties. Also is explained the correspondence between T c , the resonance-mode energy, and the “nodal gap”.

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References

  1. Takagi, H., Batlogg, B., Kao, H.L., Kwo, J., Cava, R.J., Krajewski, J.J., Peck, W.F., Jr.: Phys. Rev. Lett. 69, 2975 (1992)

    Article  ADS  Google Scholar 

  2. Kubo, Y., Manako, T.: Physica C 197, 378 (1992)

    Article  ADS  Google Scholar 

  3. Hwang, H.Y., Batlogg, B., Takagi, H., Kao, H.L., Kwo, J., Cava, R.J., Krajewski, J.J., Peck, W.F., Jr.: Phys. Rev. Lett. 72, 2636 (1994)

    Article  ADS  Google Scholar 

  4. Fisher, B., Genossar, J., Lelong, I.O., Kessel, A., Ashkenazi, J.: J. Supercond. 1, 53 (1988)

    Article  ADS  Google Scholar 

  5. Genossar, J., Fisher, B., Lelong, I.O., Ashkenazi, J., Patlagan, L.: Physica C 157, 320 (1989)

    Article  ADS  Google Scholar 

  6. Tanaka, S., Sera, M., Sato, M., Fujishita, H.: J. Phys. Soc. Jpn. 61, 1271 (1992)

    Article  ADS  Google Scholar 

  7. Matsuura, K., Wada, T., Yaegashi, Y., Tajima, S., Yamauchi, H.: Phys. Rev. B 46, 11923 (1992)

    Article  ADS  Google Scholar 

  8. Obertelli, S.D., Cooper, J.R., Tallon, J.L.: Phys. Rev. B 46, 14928 (1992)

    Article  ADS  Google Scholar 

  9. Subramaniam, C.K., Kaiser, A.B., Trodahl, H.J., Mawdsley, A., Buckley, R.G.: Physica C 203, 298 (1992)

    Article  Google Scholar 

  10. Puchkov, A.V., Basov, D.N., Timusk, T.: J. Phys., Condens. Matter 8, 10049 (1996)

    Article  ADS  Google Scholar 

  11. Bonn, D.A., Ruixing, Liang, Riseman, T.M., Baar, D.J., Morgan, D.C., Zhang, Kuan, Dosanjh, P., Duty, T.L., MacFarlane, A., Morris, G.D., Brewer, J.H., Hardy, W.N., Kallin, C., Berlinsky, A.J.: Phys. Rev. B 47, 11314 (1993)

    Article  ADS  Google Scholar 

  12. Zasadzinski, J.F., Ozyuzer, L., Miyakawa, N., Gray, K.E., Hinks, D.G., Kendziora, C.: Phys. Rev. Lett. 87, 067005 (2001)

    Article  ADS  Google Scholar 

  13. Luo, H.G., Su, Y.H., Xiang, T.: Phys. Rev. B 77, 014529 (2008)

    Article  ADS  Google Scholar 

  14. Tanner, D.B., Liu, H.L., Quijada, M.A., Zibold, A.M., Berger, H., Kelley, R.J., Onellion, M., Chou, F.C., Johnston, D.C., Rice, J.P., Ginsberg, D.M., Markert, J.T.: Physica B 244, 1 (1998)

    Article  ADS  Google Scholar 

  15. Boebinger, G.S., Ando, Yoichi, Passner, A., Kimura, T., Okuya, M., Shimoyama, J., Kishio, K., Tamasaku, K., Ichikawa, N., Uchida, S.: Phys. Rev. Lett. 77, 5417 (1996)

    Article  ADS  Google Scholar 

  16. Anderson, P.W.: Phys. Rev. Lett. 64, 1839 (1990)

    Article  ADS  Google Scholar 

  17. Varma, C.M., Littlewood, P.B., Schmitt-Rink, S., Abrahams, E., Ruckenstein, A.E.: Phys. Rev. Lett. 63, 1989 (1996)

    Google Scholar 

  18. Lee, Patrick A.: Rep. Prog. Phys. 71, 012501 (2008)

    Article  ADS  Google Scholar 

  19. Le Hur, Karyn, Rice, T. Maurice: Ann. Phys. 324, 1452 (2009)

    Article  ADS  MATH  Google Scholar 

  20. Ashkenazi, J.: J. Supercond. Nov. Magn 22, 3 (2009). arXiv:0809.4237

    Article  Google Scholar 

  21. Barnes, S.E.: Adv. Phys. 30, 801 (1981)

    Article  ADS  Google Scholar 

  22. Tranquada, J.M., Axe, J.D., Ichikawa, N., Nakamura, Y., Uchida, S., Nachumi, B.: Phys. Rev. B 54, 7489 (1996)

    Article  ADS  Google Scholar 

  23. Tranquada, J.M., Axe, J.D., Ichikawa, N., Moodenbaugh, A.R., Nakamura, Y., Uchida, S.: Phys. Rev. Lett. 78, 338 (1997)

    Article  ADS  Google Scholar 

  24. Yamada, K., Lee, C.H., Kurahashi, K., Wada, J., Wakimoto, S., Ueki, S., Kimura, H., Endoh, Y., Hosoya, S., Shirane, G., Birgeneau, R.J., Greven, M., Kastner, M.A., Kim, Y.J.: Phys. Rev. B 57, 6165 (1998)

    Article  ADS  Google Scholar 

  25. Howald, C., Eisaki, H., Kaneko, N., Greven, M., Kapitulnik, A.: Phys. Rev. B 67, 014533 (2003)

    Article  ADS  Google Scholar 

  26. Fang, A., Howald, C., Kaneko, N., Greven, M., Kapitulnik, A.: Phys. Rev. B 70, 214514 (2004)

    Article  ADS  Google Scholar 

  27. Hanaguri, T., Lupien, C., Kohsaka, Y., Lee, D.-H., Azuma, M., Takano, M., Takagi, H., Davis, J.C.: Nature 430, 1001 (2004)

    Article  ADS  Google Scholar 

  28. Kohsaka, Y., Taylor, C., Fujita, K., Schmidt, A., Lupien, C., Hanaguri, T., Azuma, M., Takano, M., Eisaki, H., Takagi, H., Uchida, S., Davis, J.C.: Science 315, 1380 (2007)

    Article  ADS  Google Scholar 

  29. Wise, W.D., Boyer, M.C., Chatterjee, Kamalesh, Kondo, Takeshi, Takeuchi, T., Ikuta, H., Yayu, Wang, Hudson, E.W.: Nat. Phys. 4, 696 (2008)

    Article  Google Scholar 

  30. Bickers, N.E., Scalapino, D.J., White, S.R.: Phys. Rev. Lett. 62, 961 (1989)

    Article  ADS  Google Scholar 

  31. Manske, D., Eremin, I., Bennemann, K.H.: Phys. Rev. B 67, 134520 (2003)

    Article  ADS  Google Scholar 

  32. Migdal, A.B.: Sov. Phys.—JETP 7, 996 (1958)

    MathSciNet  Google Scholar 

  33. Eliashberg, G.M.: Sov. Phys.—JETP 11, 966 (1960)

    Google Scholar 

  34. Scalapino, D.J., Schrieffer, J.R., Wilkins, J.W.: Phys. Rev. 148, 263 (1966)

    Article  ADS  Google Scholar 

  35. Andersen, O.K., Liechtenstein, A.I., Jepsen, O., Paulsen, F.: J. Phys. Chem. Solids 56, 1573 (1995)

    Article  ADS  Google Scholar 

  36. Pavarini, E., Dasgupta, I., Saha-Dasgupta, T., Jepsen, O., Andersen, O.K.: Phys. Rev. Lett. 87, 047003 (2001)

    Article  ADS  Google Scholar 

  37. Markiewicz, R.S., Sahrakorpi, S., Lindroos, M., Lin, Hsin, Bansil, A.: Phys. Rev. B 72, 054519 (2005)

    Article  ADS  Google Scholar 

  38. Ashcroft, Neil W., Mermin, N. David: Solid State Physics. Saunders College, Philadelphia (1976)

    Google Scholar 

  39. Zhang, F.C., Rice, T.M.: Phys. Rev. B 37, 3759 (1987)

    Article  ADS  Google Scholar 

  40. Ashkenazi, J.: J. Supercond. 7, 719 (1994)

    Article  ADS  Google Scholar 

  41. Ashkenazi, J.: J. Phys. Chem. Solids 63, 2333 (2002)

    Article  ADS  Google Scholar 

  42. Ashkenazi, J.: J. Phys. Chem. Solids 65, 1461 (2004); in: New Challenges in Superconductivity: Experimental Advances and Emerging Theories, Ashkenazi, J., Eremin, M.V., Cohn, J.L., Eremin, I., Manske, D., Pavuna, D., Zuo, F. Springer, p. 187 (2005)

    Article  ADS  Google Scholar 

  43. Anisimov, V.I., Korotin, M.A., Nekrasov, I.A., Pchelkina, Z.V., Sorella, S.: Phys. Rev. B 66, 100502 (2002)

    Article  ADS  Google Scholar 

  44. Wan, Xiangang, Maier, Thomas A., Savrasov, Sergej Y.: Phys. Rev. B 79, 155114 (2009)

    Article  ADS  Google Scholar 

  45. Goldstein, Herbert: Classical Mechanics, 3rd edn. Addison-Wesley, New York (1980)

    MATH  Google Scholar 

  46. Van Vliet, Carolyne M.: Equilibrium and Non-equilibrium Statistical Mechanics. World Scientific, Singapore (2008)

    Google Scholar 

  47. Mahan, Gerald D.: Many-Particle Physics, Third Edition. Kluwer Academics/Plenum Publishers, New York (2000)

    Google Scholar 

  48. Honma, T., Hor, P.H.: Phys. Rev. B 77, 184520 (2008)

    Article  ADS  Google Scholar 

  49. Zaanen, J., Gunnarsson, O.: Phys. Rev. B 40, 7391 (1989)

    Article  ADS  Google Scholar 

  50. Machida, K.: Physica C 158, 192 (1989)

    Article  ADS  Google Scholar 

  51. Emery, V.J., Kivelson, S.A.: Physica C 209, 597 (1993)

    Article  ADS  Google Scholar 

  52. Goldstone, Jeffrey, Abdus, Salam, Weinberg, Steven: Phys. Rev. 127, 965 (1962)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  53. Nakayama, K., Sato, T., Dobashi, T., Terashima, K., Souma, S., Matsui, H., Takahashi, T., Campuzano, J.C., Kudo, K., Sasaki, T., Kobayashi, N., Kondo, T., Takeuchi, T., Kadowaki, K., Kofu, M., Hirota, K.: Phys. Rev. B 74, 054505 (2006)

    Article  ADS  Google Scholar 

  54. Palczewski, A.D., Kondo, T., Khasanov, R., Kolesnikov, N.N., Timonina, A.V., Rotenberg, E., Ohta, T., Bendounan, A., Sassa, Y., Fedorov, A., Pailhis, S., Santander-Syro, A.F., Chang, J., Shi, M., Mesot, J., Fretwell, H.M., Kaminski, A.: Phys. Rev. B 78, 054523 (2008)

    Article  ADS  Google Scholar 

  55. Chang, J., Sassa, Y., Guerrero, S., Mansson, M., Shi, M., Pailhes, S., Bendounan, A., Mottl, R., Claesson, T., Tjernberg, O., Patthey, L., Ido, M., Momono, N., Oda, M., Mudry, C., Mesot, J.: New J. Phys. 10, 103016 (2008)

    Article  ADS  Google Scholar 

  56. Doiron-Leyraud, N., Proust, C., LeBoeuf, D., Levallois, J., Bonnemaison, J.-B., Ruixing, L., Bonn, D.A., Hardy, W.N., Taillefer, L.: Nature 447, 565 (2007)

    Article  ADS  Google Scholar 

  57. Yelland, E.A., Singleton, J., Mielke, C.H., Harrison, N., Balakirev, F.F., Dabrowski, B., Cooper, J.R.: Phys. Rev. Lett. 100, 047003 (2008)

    Article  ADS  Google Scholar 

  58. Vignolle, B., Carrington, A., Cooper, R.A., French, M.M.J., Mackenzie, A.P., Jaudet, C., Vignolles, D., Proust, Cyril, Hussey, N.E.: Nature 455, 952 (2008)

    Article  ADS  Google Scholar 

  59. Xie, B.P., Yang, K., Shen, D.W., Zhao, J.F., Ou, H.W., Wei, J., Gu, S.Y., Arita, M., Qiao, S., Namatame, H., Taniguchi, M., Kaneko, N., Eisaki, H., Tsuei, K.D., Cheng, C.M., Vobornik, I., Fujii, J., Rossi, G., Yang, Z.Q., Feng, D.L.: Phys. Rev. Lett. 98, 147001 (2007)

    Article  ADS  Google Scholar 

  60. Meevasana, W., Baumberger, F., Tanaka, K., Schmitt, F., Dunkel, W.R., Lu, D.H., Mo, S.-K., Eisaki, H., Shen, Z.-X.: Phys. Rev. B 77, 104506 (2008)

    Article  ADS  Google Scholar 

  61. Chang, J., Shi, M., Pailhis, S., Mensson, M., Claesson, T., Tjernberg, O., Bendounan, A., Sassa, Y., Patthey, L., Momono, N., Oda, M., Ido, M., Guerrero, S., Mudry, C., Mesot, J.: Phys. Rev. B 78, 205103 (2008)

    Article  ADS  Google Scholar 

  62. Valla, T., Fedorov, A.V., Johnson, P.D., Wells, B.O., Hulbert, S.L., Li, Q., Gu, G.D., Koshizuka, N.: Science 285, 2110 (1999)

    Article  Google Scholar 

  63. van der Marel, D., Molegraaf, H.J.A., Zaanen, J., Nussinov, Z., Carbone, F., Damascelli, A., Eisaki, H., Greven, M., Kes, P.H., Li, M.: Nature 425, 271 (2003)

    Article  ADS  Google Scholar 

  64. Bar-Ad, S., Fisher, B., Ashkenazi, J., Genossar, J.: Physica C 156, 741 (1988)

    Article  ADS  Google Scholar 

  65. Hwang, J., Timusk, T., Puchkov, A.V., Wang, N.L., Gu, G.D., Homes, C.C., Tu, J.J., Eisaki, H.: Phys. Rev. B 69, 094520 (2004)

    Article  ADS  Google Scholar 

  66. Kanigel, A., Chatterjee, U., Randeria, M., Norman, M.R., Koren, G., Kadowaki, K., Campuzanol, J.C.: Phys. Rev. Lett. 101, 137002 (2008)

    Article  ADS  Google Scholar 

  67. Yang, H.-B., Rameau, J.D., Johnson, P.D., Valla, T., Tsvelik, A., Gu, G.D.: Nature 456, 77 (2008)

    Article  ADS  Google Scholar 

  68. Meng, J., Liu, G., Zhang, W., Zhao, L., Liu, H., Jia, X., Mu, D., Liu, S., Dong, X., Zhang, J., Lu, W., Wang, G., Zhou, Y., Zhu, Y., Wang, X., Xu, Z., Chen, C., Zhou, X.J.: Nature 462, 335 (2009)

    Article  ADS  Google Scholar 

  69. Kanigel, A., Norman, M.R., Randeria, M., Chatterjee, U., Souma, S., Kaminski, A., Fretwell, H.M., Rosenkranz, S., Shi, M., Sato, T., Takahashi, T., Li, Z.Z., Raffy, H., Kadowaki, K., Hinks, D., Ozyuzer, L., Campuzano, J.C.: Nat. Phys. 2, 447 (2006)

    Article  Google Scholar 

  70. Chatterjee, U., Shi, M., Ai, D., Zhao, J., Kanigel, A., Rosenkranz, S., Raffy, H., Li, Z.Z., Kadowaki, K., Hinks, D.G., Xu, Z.J., Wen, J.S., Gu, G., Lin, C.T., Claus, H., Norman, M.R., Randeria, M., Campuzano, J.C.: arXiv:0910.1648

  71. Kresin, V.Z., Wolf, S.A.: Rev. Mod. Phys. 81, 481 (2009)

    Article  ADS  Google Scholar 

  72. Bourges, Ph., Keimer, B., Pailhès, S., Regnault, L.P., Sidis, Y., Ulrich, C.: arXiv:cond-mat/0211227

  73. Sidis, Y., Pailhès, S., Keimer, B., Bourges, P., Ulrich, C., Regnault, L.P.: Phys. Status Solidi (b) 241, 1204 (2004)

    Article  ADS  Google Scholar 

  74. van Heumen, E., Muhlethaler, E., Kuzmenko, A.B., Eisaki, H., Meevasana, W., Greven, M., van der Marel, D.: Phys. Rev. B 79, 184512 (2009)

    Article  ADS  Google Scholar 

  75. Le Tacon, M., Sacuto, A., Georges, A., Kotliar, G., Gallais, Y., Colson, D., Forget, A.: Nat. Phys. 2, 537 (2006)

    Article  Google Scholar 

  76. Guyard, W., Sacuto, A., Cazayous, M., Gallais, Y., Le Tacon, M., Colson, D., Forget, A.: Phys. Rev. Lett. 101, 097003 (2008)

    Article  ADS  Google Scholar 

  77. Hüfner, S., Hossain, M.A., Damascelli, A., Sawatzky, G.A.: Rep. Prog. Phys. 71, 062501 (2008)

    Article  ADS  Google Scholar 

  78. Lee, W.S., Vishik, I.M., Tanaka, K., Lu, D.H., Sasagawa, T., Nagaosa, N., Devereaux, T.P., Hussain, Z., Shen, Z.-X.: Nature 450, 81 (2007)

    Article  ADS  Google Scholar 

  79. Kondo, T., Khasanov, R., Takeuchi, T., Schmalian, J., Kaminski, A.: Nature 457, 296 (2009)

    Article  ADS  Google Scholar 

  80. Nakayama, K., Sato, T., Sekiba, Y., Terashima, K., Richard, P., Takahashi, T., Kudo, K., Okumura, N., Sasaki, T., Kobayashi, N.: Phys. Rev. Lett. 102, 227006 (2009)

    Article  ADS  Google Scholar 

  81. Blanc, S., Gallais, Y., Sacuto, A., Cazayous, M., Miasson, M.A., Gu, G.D., Wen, J.S., Xu, Z.J.: Phys. Rev. B 80, 140502 (2009)

    Article  ADS  Google Scholar 

  82. Jenkins, N., Fasano, Y., Berthod, C., Maggio-Aprile, I., Piriou, A., Giannini, E., Hoogenboom, B.W., Hess, C., Cren, T., Fischer, O.: Phys. Rev. Lett. 103, 227001 (2009)

    Article  ADS  Google Scholar 

  83. Sato, T., Matsui, H., Takahashi, T., Ding, H., Yang, H.-B., Wang, S.-C., Fujii, T., Watanabe, T., Matsuda, A., Terashima, T., Kadowaki, K.: Phys. Rev. Lett. 91, 157003 (2003)

    Article  ADS  Google Scholar 

  84. Khasanov, R., Shengelaya, A., Di Castro, D., Morenzoni, E., Maisuradze, A., Savić, I.M., Conder, K., Pomjakushina, E., Bussmann-Holder, A., Keller, H.: Phys. Rev. Lett. 101, 077001 (2008)

    Article  ADS  Google Scholar 

  85. Keller, H., Bussmann-Holder, A.: Advances in Condensed Matter Physics. Hindawi Publishing Corporation (2010), doi:10.1155/2010/393526

  86. McElroy, K., Lee, D.-H., Hoffman, J.E., Lang, K.M., Lee, J., Hudson, E.W., Eisaki, H., Uchida, S., Davis, J.C.: Phys. Rev. Lett. 94, 197005 (2005)

    Article  ADS  Google Scholar 

  87. Schachinger, E., Carbotte, J.P.: Phys. Rev. B 80, 094521 (2009)

    Article  ADS  Google Scholar 

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    J. Ashkenazi

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Ashkenazi, J. A Theory for the High-T c Cuprates: Anomalous Normal-State and Spectroscopic Properties, Phase Diagram, and Pairing. J Supercond Nov Magn 24, 1281–1308 (2011). https://doi.org/10.1007/s10948-010-0823-8

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