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The Fermi Liquid Breakdown: High-\(T_c\) Superconductivity

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Condensed Matter Applications of AdS/CFT

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Abstract

The Fermi liquid theory that we have outlined in the previous Section has been tremendously successful in explaining almost all metallic states in nature. However, fortunately nature hides always great surprises.

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Notes

  1. 1.

    See [2] for a theoretical review on BCS.

  2. 2.

    This is done in light of the holographic analysis of the normal phase transport properties, performed in Part 3.

References

  1. J.G. Bednorz, K.A. Müller, Possible hightc superconductivity in the balacuo system. Zeitschrift für Phys. B Condens. Matter 64(2), 189–193 (1986)

    Article  ADS  Google Scholar 

  2. M. Tinkham, in Introduction to Superconductivity, 2nd edn., Dover Books on Physics (Dover Publications, 2004)

    Google Scholar 

  3. H. Maeda, Y. Tanaka, M. Fukutomi, T. Asano, A new high- t c oxide superconductor without a rare earth element. Jpn. J. Appl. Phys. 27(2A), L209 (1988)

    Google Scholar 

  4. M.K. Wu, J.R. Ashburn, C.J. Torng, P.H. Hor, R.L. Meng, L. Gao, Z.J. Huang, Y.Q. Wang, C.W. Chu, Superconductivity at 93 k in a new mixed-phase y-ba-cu-o compound system at ambient pressure. Phys. Rev. Lett. 58, 908–910 (1987)

    Article  ADS  Google Scholar 

  5. P. Dai, B.C. Chakoumakos, G.F. Sun, K.W. Wong, Y. Xin, D.F. Lu, Synthesis and neutron powder diffraction study of the superconductor hgba2ca2cu3o8 + by tl substitution. Phys. C Supercond. 243(34), 201–206 (1995)

    Article  ADS  Google Scholar 

  6. C.Q. Choi, in Iron Exposed as High-Temperature Superconductor (2008)

    Google Scholar 

  7. A.J. Leggett, What do we know about high \(t_c\)? Nat. Phys. 2, 134–136 (2006)

    Google Scholar 

  8. Z.-A. Ren, G.-C. Che, X.-L. Dong, J. Yang, W. Lu, W. Yi, X.-L. Shen, Z.-C. Li, L.-L. Sun, F. Zhou, Z.-X. Zhao, Superconductivity and phase diagram in iron-based arsenic-oxides refeaso 1 (re = rare-earth metal) without fluorine doping. EPL Europhys. Lett. 83(1), 17002 (2008)

    Google Scholar 

  9. N.W. Ashcroft, N.D. Mermin, Solid State Physics (Saunders College, Philadelphia, 1976)

    MATH  Google Scholar 

  10. N. Barisic, M.K. Chan, Y. Li, Y. Guichuan, X. Zhao, M. Dressel, A. Smontara, M. Greven, Universal sheet resistance and revised phase diagram of the cuprate high-temperature superconductors. Proc. Natl. Acad. Sci. United States of America 110(30), 12235–12240 (2013)

    Google Scholar 

  11. R.M. Hazen, L.W. Finger, R.J. Angel, C.T. Prewitt, N.L. Ross, H.K. Mao, C.G. Hadidiacos, P.H. Hor, R.L. Meng, C.W. Chu, Crystallographic description of phases in the y-ba-cu-o superconductor. Phys. Rev. B 35, 7238–7241 (1987)

    Article  ADS  Google Scholar 

  12. A. Hermann, in Thallium-Based High-Temperature Superconductors, Applied Physics (Taylor & Francis, 1993)

    Google Scholar 

  13. N.P. Armitage, P. Fournier, R.L. Greene, Progress and perspectives on electron-doped cuprates. Rev. Mod. Phys. 82, 2421–2487 (2010)

    Article  ADS  Google Scholar 

  14. E. Pavarini, I. Dasgupta, T. Saha-Dasgupta, O. Jepsen, O.K. Andersen, Band-structure trend in hole-doped cuprates and correlation with \({{t}}_{{c}}\)max. Phys. Rev. Lett. 87, 047003 (2001)

    Article  ADS  Google Scholar 

  15. H.-Q. Ding, Could in-plane exchange anisotropy induce the observed antiferromagnetic transitions in the undoped high-\({{t}}_{{c}}\) materials? Phys. Rev. Lett. 68, 1927–1930 (1992)

    Article  ADS  Google Scholar 

  16. M.A. Kastner, R.J. Birgeneau, G. Shirane, Y. Endoh, Magnetic, transport, and optical properties of monolayer copper oxides. Rev. Mod. Phys. 70, 897–928 (1998)

    Article  ADS  Google Scholar 

  17. T. Thio, T.R. Thurston, N.W. Preyer, P.J. Picone, M.A. Kastner, H.P. Jenssen, D.R. Gabbe, C.Y. Chen, R.J. Birgeneau, A. Aharony, Antisymmetric exchange and its influence on the magnetic structure and conductivity of \({\text{la}}_{2}cu{\text{ o }}_{4}\). Phys. Rev. B 38, 905–908 (1988)

    Google Scholar 

  18. T. Yildirim, A.B. Harris, O. Entin-Wohlman, and Amnon Aharony, Spin structures of tetragonal lamellar copper oxides. Phys. Rev. Lett. 72, 3710–3713 (1994)

    Article  ADS  Google Scholar 

  19. C. Hartiger, in Doping Dependence of Phase Transitions and Ordering Phenomena in Cuprate Superconductors, DFG FG 538 (2009)

    Google Scholar 

  20. M.R. Presland, General trends in oxygen stoichiometry effects on tc in bi and tl superconductors. Phys. C Supercond. 176(13), 95–105 (1991)

    Google Scholar 

  21. J.L. Tallon, C. Bernhard, H. Shaked, R.L. Hitterman, J.D. Jorgensen, Generic superconducting phase behavior in high-\({{t}}_{{c}}\) cuprates: \({{t}}_{{c}}\) variation with hole concentration in \({\text{ yba }}_{2}{\text{ cu }}_{3}{\text{ o }}_{7{{-}}{{\delta }}}\). Phys. Rev. B 51, 12911–12914 (1995)

    Article  ADS  Google Scholar 

  22. C.C. Tsuei, J.R. Kirtley, Pairing symmetry in cuprate superconductors. Rev. Mod. Phys. 72, 969–1016 (2000)

    Article  ADS  Google Scholar 

  23. D.J. Van Harlingen, Phase-sensitive tests of the symmetry of the pairing state in the high-temperature superconductors-evidence for \({d}_{{x}^{2}{-}{y}^{2}}\) symmetry. Rev. Mod. Phys. 67, 515–535 (1995)

    Article  ADS  Google Scholar 

  24. N.-C. Yeh, C.-T. Chen, G. Hammerl, J. Mannhart, A. Schmehl, C.W. Schneider, R.R. Schulz, S. Tajima, K. Yoshida, D. Garrigus, M. Strasik, Evidence of doping-dependent pairing symmetry in cuprate superconductors. Phys. Rev. Lett. 87, 087003 (2001)

    Article  ADS  Google Scholar 

  25. T. Timusk, B. Statt, The pseudogap in high-temperature superconductors: an experimental survey. Rep. Prog. Phys. 62(1), 61 (1999)

    Google Scholar 

  26. J. Loram, Evidence on the pseudogap and condensate from the electronic specific heat. J. Phys. Chem. Solids 62, 59–64 (2001)

    Article  ADS  Google Scholar 

  27. J.W. Loram, K.A. Mirza, J.R. Cooper, W.Y. Liang, Electronic specific heat of \({\text{ yba }}_{2}{\text{ cu }}_{3}{\text{ o }}_{6+{x}}\) from 1.8 to 300 k. Phys. Rev. Lett. 71, 1740–1743 (1993)

    Article  ADS  Google Scholar 

  28. J.W. Loram, K.A. Mirza, J.R. Cooper, W.Y. Liang, J.M. Wade, Electronic specific heat of yba2cu3o6+x from 1.8 to 300 k. J. Supercond. 7(1), 243–249 (1994)

    Article  ADS  Google Scholar 

  29. D.N. Basov, T. Timusk, Electrodynamics of high-\({T}_{c}\) superconductors. Rev. Mod. Phys. 77, 721–779 (2005)

    Article  ADS  Google Scholar 

  30. N.E. Hussey, K. Takenaka, H. Takagi, Universality of the mottiofferegel limit in metals. Phil. Mag. 84(27), 2847–2864 (2004)

    Article  ADS  Google Scholar 

  31. K. Takenaka, J. Nohara, R. Shiozaki, S. Sugai, Incoherent charge dynamics of \({\text{ la }}_{2{-}x}{\text{ sr }}_{x}{\text{ cuo }}_{4}:\) dynamical localization and resistivity saturation. Phys. Rev. B 68, 134501 (2003)

    Article  ADS  Google Scholar 

  32. J. Orenstein, G.A. Thomas, A.J. Millis, S.L. Cooper, D.H. Rapkine, T. Timusk, L.F. Schneemeyer, J.V. Waszczak, Frequency- and temperature-dependent conductivity in \({\text{ yba }}_{2}{\text{ cu }}_{3}{\text{ o }}_{6+{x}}\) crystals. Phys. Rev. B 42, 6342–6362 (1990)

    Google Scholar 

  33. B. Bucher, P. Steiner, J. Karpinski, E. Kaldis, P. Wachter, Influence of the spin gap on the normal state transport in \({\text{ yba }}_{2}{\text{ cu }}_{4}{\text{ o }}_{8}\). Phys. Rev. Lett. 70, 2012–2015 (1993)

    Article  ADS  Google Scholar 

  34. N.E. Hussey, K. Nozawa, H. Takagi, S. Adachi, K. Tanabe, Anisotropic resistivity of \({\text{ yba }}_{2}{\text{ cu }}_{4}{\text{ o }}_{8}\): Incoherent-to-metallic crossover in the out-of-plane transport. Phys. Rev. B 56, R11423–R11426 (1997)

    Article  ADS  Google Scholar 

  35. T. Ito, K. Takenaka, S. Uchida, Systematic deviation from t-linear behavior in the in-plane resistivity of \({\text{ yba }}_{2}{\text{ cu }}_{3}{\text{ o }}_{7{-}}{y}\): Evidence for dominant spin scattering. Phys. Rev. Lett. 70, 3995–3998 (1993)

    Article  ADS  Google Scholar 

  36. Y. Ando, G.S. Boebinger, A. Passner, T. Kimura, K. Kishio, Logarithmic divergence of both in-plane and out-of-plane normal-state resistivities of superconducting \({\text{ la }}_{2{-}x}{\text{ sr }}_{x}\text{ Cu }{\text{ o }}_{4}\) in the zero-temperature limit. Phys. Rev. Lett. 75, 4662–4665 (1995)

    Google Scholar 

  37. G.S. Boebinger, Y. Ando, A. Passner, T. Kimura, M. Okuya, J. Shimoyama, K. Kishio, K. Tamasaku, N. Ichikawa, S. Uchida, Insulator-to-metal crossover in the normal state of \({\text{ la }}_{2{-}{x}}{\text{ sr }}_{{x}}{\text{ cuo }}_{4}\) near optimum doping. Phys. Rev. Lett. 77, 5417–5420 (1996)

    Google Scholar 

  38. S. Ono, Y. Ando, T. Murayama, F.F. Balakirev, J.B. Betts, G.S. Boebinger, Metal-to-insulator crossover in the low-temperature normal state of \({{\text{ Bi }}_{2}\text{ Sr }}_{2{-}{x}}{\text{ la }}_{{x}}{\text{ cuo }}_{6+{\delta }}\). Phys. Rev. Lett. 85, 638–641 (2000)

    Google Scholar 

  39. A.P. Mackenzie, S.R. Julian, D.C. Sinclair, C.T. Lin, Normal-state magnetotransport in superconducting \({\text{ tl }}_{2}{\text{ ba }}_{2}{\text{ cuo }}_{6+{{\delta }}}\) to millikelvin temperatures. Phys. Rev. B 53, 5848–5855 (1996)

    Article  ADS  Google Scholar 

  40. T. Manako, Y. Kubo, Y. Shimakawa, Transport and structural study of \({\text{ tl }}_{2}{\text{ ba }}_{2}{\text{ cuo }}_{6+{{\delta }}}\) single crystals prepared by the kcl flux method. Phys. Rev. B 46, 11019–11024 (1992)

    Google Scholar 

  41. S.H. Naqib, J.R. Cooper, J.L. Tallon, C. Panagopoulos, Temperature dependence of electrical resistivity of high-tc cupratesfrom pseudogap to overdoped regions. Phys. C Supercond. 387(34), 365–372 (2003)

    Article  ADS  Google Scholar 

  42. A. Kaminski, S. Rosenkranz, H.M. Fretwell, Z.Z. Li, H. Raffy, M. Randeria, M.R. Norman, J.C. Campuzano, Crossover from coherent to incoherent electronic excitations in the normal state of \({\text{ b }\text{ i }}_{2}{\text{ s }\text{ r }}_{2}{\text{ c }\text{ a }\text{ c }\text{ u }}_{2}{\text{ o }}_{8+{\delta }}\). Phys. Rev. Lett. 90, 207003 (2003)

    Article  ADS  Google Scholar 

  43. A.A. Abrikosov, in Introduction to the Theory of Normal Metals, Solid State Physics Series (Academic Press, 1972)

    Google Scholar 

  44. T.R. Chien, Z.Z. Wang, N.P. Ong, Effect of zn impurities on the normal-state hall angle in single-crystal \({\text{ yba }}_{2}{\text{ cu }}_{3{{-}}{x}}{\text{ zn }}_{{x}}{\text{ o }}_{7{{-}}{{\delta }}}\). Phys. Rev. Lett. 67, 2088–2091 (1991)

    Article  ADS  Google Scholar 

  45. H.Y. Hwang, B. Batlogg, H. Takagi, H.L. Kao, J. Kwo, R.J. Cava, J.J. Krajewski, W.F. Peck, Scaling of the temperature dependent hall effect in \({\text{ la }}_{2{{-}}{x}}{\text{ sr }}_{{x}}{\text{ cuo }}_{4}\). Phys. Rev. Lett. 72, 2636–2639 (1994)

    Article  ADS  Google Scholar 

  46. G. Xiao, P. Xiong, M.Z. Cieplak, Universal hall effect in \({\text{ la }}_{1.85}{\text{ sr }}_{0.15}{\text{ cu }}_{1{{-}}{x}}{{a}}_{{x}}{\text{ o }}_{4}\) systems (a=fe, co, ni, zn, ga). Phys. Rev. B 46, 8687–8690 (1992)

    Google Scholar 

  47. Y. Ando, T. Murayama, Nonuniversal power law of the hall scattering rate in a single-layer cuprate \({\text{ bi }}_{2}{\text{ sr }}_{2{-}x}{\text{ la }}_{x}{\text{ cuo }}_{6}\). Phys. Rev. B 60, R6991–R6994 (1999)

    Google Scholar 

  48. J.M. Harris, Y.F. Yan, P. Matl, N.P. Ong, P.W. Anderson, T. Kimura, K. Kitazawa, Violation of kohler’s rule in the normal-state magnetoresistance of \({\text{ yba }}_{2}{\text{ cu }}_{3}{O}_{7{-}{{\delta }}} and {\text{ la }}_{2}{\text{ sr }}_{x}{\text{ cuo }}_{4}\). Phys. Rev. Lett. 75, 1391–1394 (1995)

    Article  ADS  Google Scholar 

  49. T. Kimura, S. Miyasaka, H. Takagi, K. Tamasaku, H. Eisaki, S. Uchida, K. Kitazawa, M. Hiroi, M. Sera, N. Kobayashi, In-plane and out-of-plane magnetoresistance in \({\text{ la }}_{2{{-}}{x}}{\text{ sr }}_{{x}}{\text{ cuo }}_{4}\) single crystals. Phys. Rev. B 53, 8733–8742 (1996)

    Article  ADS  Google Scholar 

  50. K.H. Bennemann, J.B. Ketterson, in The Physics of Superconductors: Conventional and High-tc Superconductors, Conventional and High-Tc Superconductors (Springer, Heidelberg, 2003)

    Google Scholar 

  51. S.D. Obertelli, J.R. Cooper, J.L. Tallon, Systematics in the thermoelectric power of high-\({{t}}_{{c}}\) oxides. Phys. Rev. B 46, 14928–14931 (1992)

    Article  ADS  Google Scholar 

  52. Y. Ando, Y. Hanaki, S. Ono, T. Murayama, K. Segawa, N. Miyamoto, S. Komiya, Carrier concentrations in \({\text{ bi }}_{2}{\text{ sr }}_{2{-}z}{\text{ la }}_{z}{\text{ cuo }}_{6+{\delta }}\) single crystals and their relation to the hall coefficient and thermopower. Phys. Rev. B 61, R14956–R14959 (2000)

    Google Scholar 

  53. S. Hod, Radiative tail of realistic rotating gravitational collapse. Phys. Rev. Lett. 84, 10–13 (2000)

    Google Scholar 

  54. M. Matusiak, K. Rogacki, B.W. Veal, Enhancement of the hall-lorenz number in optimally doped yba \(_{2}cu_{3}o_{7-d}\). EPL 88(4), 47005 (2009)

    Google Scholar 

  55. N. Khare, in Handbook of High-Temperature Superconductor Electronics (Dekker, Abingdon, 2003)

    Google Scholar 

  56. T. Nakano, N. Momono, M. Oda, M. Ido, Correlation between the doping dependences of superconducting gap magnitude 2 0 and pseudogap temperature t* in high-t c cuprates. J. Phys. Soc. Jpn. 67(8), 2622–2625 (1998)

    Google Scholar 

  57. T. Watanabe, T. Fujii, A. Matsuda, Anisotropic resistivities of precisely oxygen controlled single-crystal \({\text{ bi }}_{2}{\text{ sr }}_{2}{\text{ cacu }}_{2}{O}_{8+{{\delta }}}\): Systematic study on "spin gap" effect. Phys. Rev. Lett. 79, 2113–2116 (1997)

    Article  ADS  Google Scholar 

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Amoretti, A. (2017). The Fermi Liquid Breakdown: High-\(T_c\) Superconductivity. In: Condensed Matter Applications of AdS/CFT. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-61875-3_3

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