Review Article | Published:

From quantum matter to high-temperature superconductivity in copper oxides

Nature volume 518, pages 179186 (12 February 2015) | Download Citation

Abstract

The discovery of high-temperature superconductivity in the copper oxides in 1986 triggered a huge amount of innovative scientific inquiry. In the almost three decades since, much has been learned about the novel forms of quantum matter that are exhibited in these strongly correlated electron systems. A qualitative understanding of the nature of the superconducting state itself has been achieved. However, unresolved issues include the astonishing complexity of the phase diagram, the unprecedented prominence of various forms of collective fluctuations, and the simplicity and insensitivity to material details of the ‘normal’ state at elevated temperatures.

Access optionsAccess options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

References

  1. 1.

    & Possible high Tc superconductivity in the Ba-La-Cu-O system. Z. Phys. B 64, 189–193 (1986)

  2. 2.

    , & Theory of superconductivity. Phys. Rev. 108, 1175–1204 (1957)

  3. 3.

    & Comments on the maximum superconducting transition temperature. In Superconductivity in d- and f-band Metals (ed. ) 17–27 (American Institute of Physics, 1972)

  4. 4.

    , , , & Superconductivity at 39 K in magnesium diboride. Nature 410, 63–64 (2001)

  5. 5.

    , , , & Phenomenology of the normal state of Cu-O high-temperature superconductors. Phys. Rev. Lett. 63, 1996–1999 (1989)

  6. 6.

    , & Universality of the Mott-Ioffe-Regel limit of metals. Phil. Mag. 84, 2847–2864 (2004)

  7. 7.

    , & Theory of intertwined orders in high temperature superconductors. Preprint at (2014)

  8. 8.

    , , , & Experimental determination of the superconducting pairing state in YBCO from the phase coherence of YBCO-Pb dc SQUIDs. Phys. Rev. Lett. 71, 2134–2137 (1993)

  9. 9.

    & Pairing symmetry in cuprate superconductors. Rev. Mod. Phys. 72, 969–1016 (2000)

  10. 10.

    , & d-wave pairing near a spin-density-wave instability. Phys. Rev. B 34, 8190–8192 (1986)

  11. 11.

    , & Spin-fluctuation-mediated even-parity pairing in heavy-fermion superconductors. Phys. Rev. B 34, 6554–6556 (1986)

  12. 12.

    , & Possible superconductivity in nearly antiferromagnetic itinerant fermion systems. Phys. Rev. B 34, 7716–7720 (1986)

  13. 13.

    et al. Strength of the spin-fluctuation-mediated pairing interaction in a high-temperature superconductor. Nature Phys. 5, 217–221 (2009)

  14. 14.

    Watching rush hour in the world of electrons. Science 315, 1372–1373 (2007)

  15. 15.

    The resonating valence bond state in La2CuO4 and superconductivity. Science 235, 1196–1198 (1987)

  16. 16.

    et al. Antiferromagnetism in La2CuO4-y. Phys. Rev. Lett. 58, 2802–2805 (1987)

  17. 17.

    , & Low-temperature behavior of two-dimensional quantum antiferromagnets. Phys. Rev. Lett. 60, 1057–1060 (1988)

  18. 18.

    et al. Quantum oscillations and the Fermi surface in an underdoped high-Tc superconductor. Nature 447, 565–568 (2007)First quantum oscillation evidence for a distinct electronic state with a reconstructed Fermi surface, realized in the underdoped copper oxides under intense magnetic fields.

  19. 19.

    et al. Normal-state nodal electronic structure in underdoped high-Tc copper oxides. Nature 511, 61–64 (2014)

  20. 20.

    & Charged magnetic domain lines and the magnetism of high-Tc oxides. Phys. Rev. B 40, 7391–7394 (1989)

  21. 21.

    & Frustrated electronic phase separation and high-temperature superconductors. Physica C 209, 597–621 (1993)

  22. 22.

    , , , & Evidence for stripe correlations of spins and holes in copper oxide superconductors. Nature 375, 561–563 (1995)First evidence from neutron scattering for modulated spin and charge order in underdoped copper oxides.

  23. 23.

    , & Superconductivity in the repulsive Hubbard model: an asymptotically exact weak-coupling solution. Phys. Rev. B 81, 224505 (2010)

  24. 24.

    A common thread: the pairing interaction for unconventional superconductors. Rev. Mod. Phys. 84, 1383–1417 (2012)A comprehensive review of spin fluctuation pairing theories for superconductivity.

  25. 25.

    , , , & Phases of the infinite U Hubbard model on square lattices. Phys. Rev. Lett. 108, 126406 (2012)

  26. 26.

    , & Doping a Mott insulator: physics of high-temperature superconductivity. Rev. Mod. Phys. 78, 17–85 (2006)An overview of strong coupling models of copper oxides from the doped Mott insulator view, focusing on the resonating valence bond picture.

  27. 27.

    , & High-Tc superconductors: a variational theory of the superconducting state. Phys. Rev. B 70, 054504 (2004)

  28. 28.

    , , & Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions. Rev. Mod. Phys. 68, 13–125 (1996)Fundamentals of dynamical mean field theory are discussed in this authoritative review.

  29. 29.

    & Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 6.1–6.18 (2012)An introduction to density matrix renormalization group studies of two-dimensional materials, including tensor network generalizations.

  30. 30.

    & Density matrix renormalization group study of the striped phase in the 2D t-J model. Phys. Rev. Lett. 80, 1272–1275 (1998)

  31. 31.

    , & Competing states in the t-J model: uniform d-wave state versus stripe state. Phys. Rev. Lett. 113, 046402 (2014)

  32. 32.

    et al. Intense paramagnon excitations in a large family of high-temperature superconductors. Nature Phys. 7, 725–730 (2011)

  33. 33.

    et al. Persistence of magnetic excitations in La2-xSrxCuO4 from the undoped insulator to the heavily overdoped non-superconducting metal. Nature Mater. 12, 1019–1023 (2013)

  34. 34.

    et al. Spin susceptibility in underdoped YBa2Cu3O6+x. Phys. Rev. B 61, 14773–14786 (2000)

  35. 35.

    , , & Evolution of the resonance and incommensurate spin fluctuations in superconducting YBa2Cu3O6+x. Phys. Rev. B 63, 054525 (2001)

  36. 36.

    , & Bosons in high-temperature superconductors: an experimental survey. Rep. Prog. Phys. 74, 066501 (2011)

  37. 37.

    Is there glue in cuprate superconductors? Science 316, 1705–1707 (2007)

  38. 38.

    et al. Evidence for ubiquitous strong electron-phonon coupling in high-temperature superconductors. Nature 412, 510–514 (2001)

  39. 39.

    et al. Electron–phonon coupling reflecting dynamic charge inhomogeneity in copper oxide superconductors. Nature 440, 1170–1173 (2006)

  40. 40.

    A “midinfrared” scenario for cuprate superconductivity. Proc. Natl Acad. Sci. USA 96, 8365–8372 (1999)

  41. 41.

    & Contribution to the theory of superconducting alloys with paramagnetic impurities. Sov. Phys. JETP 12, 1243–1253 (1961)

  42. 42.

    , & Strong correlations make high-temperature superconductors robust against disorder. Nature Phys. 4, 762–765 (2008)

  43. 43.

    et al. Universal correlations between Tc and ns/m* in high-Tc cuprate superconductors. Phys. Rev. Lett. 62, 2317–2320 (1989)

  44. 44.

    & Importance of phase fluctuations in superconductors with small superfluid density. Nature 374, 434–437 (1995)

  45. 45.

    et al. Electronic phase diagram of high-temperature copper oxide superconductors. Proc. Natl Acad. Sci. USA 108, 9346–9349 (2011)

  46. 46.

    et al. BCS-like Bogoliubov quasiparticles in high-Tc superconductors observed by angle-resolved photoemission spectroscopy. Phys. Rev. Lett. 90, 217002 (2003)

  47. 47.

    et al. Temperature dependent photoemission studies of optimally doped Bi2Sr2CaCu2O8. Phys. Rev. Lett. 82, 2179–2182 (1999)

  48. 48.

    et al. Signature of superfluid density in the single-particle excitation spectrum of Bi2Sr2CaCu2O8+δ. Science 289, 277–281 (2000)

  49. 49.

    et al. Cu spin dynamics and superconducting precursor effects in planes above Tc in YBa2Cu3O6.7. Phys. Rev. Lett. 62, 1193–1196 (1989)

  50. 50.

    , & 89Y NMR evidence for a Fermi-liquid behavior in YBa2Cu3O6+x. Phys. Rev. Lett. 63, 1700–1703 (1989)

  51. 51.

    , , , & Optical conductivity of c axis oriented YBa2Cu3O6.70: evidence for a pseudogap. Phys. Rev. Lett. 71, 1645–1648 (1993)

  52. 52.

    , & The pseudogap state in high-Tc superconductors: an infrared study. J. Phys. Condens. Matter 8, 10049–10082 (1996)

  53. 53.

    , , , & Influence of the spin gap on the normal state transport in YBa2Cu4O8. Phys. Rev. Lett. 70, 2012–2015 (1993)

  54. 54.

    , & Systematic deviation from T-linear behavior in the in-plane resistivity of YBa2Cu3O7-y: evidence for dominant spin scattering. Phys. Rev. Lett. 70, 3995–3998 (1993)

  55. 55.

    et al. Energy gaps in high-transition-temperature cuprate superconductors. Nature Phys. 10, 483–495 (2014)

  56. 56.

    et al. Destruction of the Fermi surface in underdoped high-Tc superconductors. Nature 392, 157–160 (1998)

  57. 57.

    et al. Unconventional electronic structure evolution with hole doping in Bi2Sr2CaCu2O8+δ: angle-resolved photoemission results. Phys. Rev. Lett. 76, 4841–4844 (1996)First indication from photoemission of a pseudogap and reconstructed Fermi surface in underdoped copper oxides.

  58. 58.

    et al. Emergence of preformed Cooper pairs from the doped Mott insulating state in Bi2Sr2CaCu2O8+δ. Nature 456, 77–80 (2008)

  59. 59.

    et al. Imaging quasiparticle interference in Bi2Sr2CaCu2O8+δ. Science 297, 1148–1151 (2002)First study of quasiparticle interference in copper oxides obtained from a Fourier transform of scanning tunnelling spectra.

  60. 60.

    et al. Relating atomic-scale electronic phenomena to wave-like quasiparticle states in superconducting Bi2Sr2CaCu2O8+δ. Nature 422, 592–596 (2003)

  61. 61.

    et al. How Cooper pairs vanish approaching the Mott insulator in Bi2Sr2CaCu2O8+δ. Nature 454, 1072–1078 (2008)

  62. 62.

    et al. Simultaneous transitions in cuprate momentum-space topology and electronic symmetry breaking. Science 344, 612–616 (2014)

  63. 63.

    et al. A momentum-dependent perspective on quasiparticle interference in Bi2Sr2CaCu2O8+δ. Nature Phys. 5, 718–721 (2009)

  64. 64.

    et al. Local ordering in the pseudogap state of the high-Tc superconductor Bi2Sr2CaCu2O8+δ. Science 303, 1995–1998 (2004)

  65. 65.

    et al. Fluctuating stripes at the onset of the pseudogap in the high-Tc superconductor Bi2Sr2CaCu2O8+x. Nature 468, 677–680 (2010)

  66. 66.

    , , & Coexistence of periodic modulation of quasiparticle states and superconductivity in Bi2Sr2CaCu2O8+δ. Proc. Natl Acad. Sci. USA 100, 9705–9709 (2003)

  67. 67.

    et al. Ubiquitous interplay between charge ordering and high-temperature superconductivity in cuprates. Science 343, 393–396 (2014)

  68. 68.

    et al. Charge order driven by Fermi-arc instability in Bi2Sr2-xLaxCuO6+δ. Science 343, 390–392 (2014)

  69. 69.

    et al. Spectroscopic evidence for a pseudogap in the normal state of underdoped high-Tc superconductors. Nature 382, 51–54 (1996)

  70. 70.

    et al. Excitation gap in the normal state of underdoped Bi2Sr2CaCu2O8+δ. Science 273, 325–329 (1996)

  71. 71.

    , , , & Vanishing of phase coherence in underdoped Bi2Sr2CaCu2O8+δ. Nature 398, 221–223 (1999)

  72. 72.

    et al. Diamagnetism and Cooper pairing above Tc in cuprates. Phys. Rev. B 81, 054510 (2010)

  73. 73.

    et al. Evidence of a precursor superconducting phase at temperatures as high as 180 K in RBa2Cu3O7-δ (R = Y, Gd, Eu) superconducting crystals from infrared spectroscopy. Phys. Rev. Lett. 106, 047006 (2011)

  74. 74.

    et al. Optically induced coherent transport far above Tc in underdoped YBa2Cu3O6+δ. Phys. Rev. B 89, 184516 (2014)

  75. 75.

    et al. Modeling the Fermi arc in underdoped cuprates. Phys. Rev. B 76, 174501 (2007)

  76. 76.

    et al. The origin and non-quasiparticle nature of Fermi arcs in Bi2Sr2CaCu2O8+δ. Nature Phys. 8, 606–610 (2012)

  77. 77.

    et al. Spectroscopic fingerprint of phase-incoherent superconductivity in the underdoped Bi2Sr2CaCu2O8+δ. Science 325, 1099–1103 (2009)

  78. 78.

    , , & Hidden order in the cuprates. Phys. Rev. B 63, 094503 (2001)

  79. 79.

    & Stripe structures in the t-t′-J model. Physica C 481, 146–152 (2012)

  80. 80.

    , , & c-Axis optical response in the static stripe ordered phase of the cuprates. Phys. Rev. Lett. 86, 500–503 (2001)

  81. 81.

    , , , & Two-dimensional superconducting fluctuations in stripe-ordered La1.875Ba0.125CuO4. Phys. Rev. Lett. 99, 067001 (2007)

  82. 82.

    et al. Incommensurate spin dynamics of underdoped superconductor YBa2Cu3O6.7. Phys. Rev. Lett. 83, 608–611 (1999)

  83. 83.

    & Neutron scattering studies on stripe phases in non-cuprate materials. Physica C 481, 31–45 (2012)

  84. 84.

    et al. Spin dynamics in the pseudogap state of a high-temperature superconductor. Nature Phys. 3, 780–785 (2007)

  85. 85.

    Linear response theory and the universal nature of the magnetic excitation spectrum of the cuprates. Phys. Rev. B 75, 184514 (2007)

  86. 86.

    et al. Magnetic-field-induced charge-stripe order in the high-temperature superconductor YBa2Cu3Oy. Nature 477, 191–194 (2011)

  87. 87.

    et al. Connection between charge-density-wave order and charge transport in the cuprate superconductors. Nature Commun. 5, 5875 (2014)

  88. 88.

    et al. Long-range incommensurate charge fluctuations in (Y,Nd)Ba2Cu3O6+x. Science 337, 821–825 (2012)Demonstration of charge crystallization without spin order as a generic ordering phenomenon in underdoped copper oxides, using resonant X-ray scattering.

  89. 89.

    et al. Direct observation of competition between superconductivity and charge density wave order in YBa2Cu3O6.67. Nature Phys. 8, 871–876 (2012)

  90. 90.

    et al. Inelastic X-ray scattering in YBa2Cu3O6.6 reveals giant phonon anomalies and elastic central peak due to charge-density-wave formation. Nature Phys. 10, 52–58 (2014)

  91. 91.

    et al. Short-range charge order reveals the role of disorder in the pseudogap state of high-Tc superconductors. Preprint at (2014)

  92. 92.

    et al. Resonant X-ray scattering study of charge density wave correlations in YBa2Cu3O6+x. Phys. Rev. B 90, 054513 (2014)

  93. 93.

    , & Electronic liquid-crystal phases of a doped Mott insulator. Nature 393, 550–553 (1998)

  94. 94.

    , , & Electrical resistivity anisotropy from self-organized one dimensionality in high-temperature superconductors. Phys. Rev. Lett. 88, 137005 (2002)

  95. 95.

    et al. Broken rotational symmetry in the pseudogap phase of a high-Tc superconductor. Nature 463, 519–522 (2010)

  96. 96.

    et al. Electronic liquid crystal state in the high-temperature superconductor YBa2Cu3O6.45. Science 319, 597–600 (2008)

  97. 97.

    et al. How to detect fluctuating stripes in the high-temperature superconductors. Rev. Mod. Phys. 75, 1201–1241 (2003)A pedagogical treatise of electronic charge order and how to study it experimentally.

  98. 98.

    et al. Intra-unit-cell electronic nematicity of the high-Tc copper-oxide pseudogap states. Nature 466, 347–351 (2010)

  99. 99.

    et al. Detection of electronic nematicity using scanning tunneling microscopy. Phys. Rev. B 87, 161117 (2013)

  100. 100.

    et al. Magnetic order in the pseudogap phase of high-Tc superconductors. Phys. Rev. Lett. 96, 197001 (2006)

  101. 101.

    Non-Fermi-liquid states and pairing instability of a general model of copper oxide metals. Phys. Rev. B 55, 14554–14580 (1997)

  102. 102.

    et al. Polar Kerr-effect measurements of the high-temperature YBa2Cu3O6+x superconductor: evidence for broken symmetry near the pseudogap temperature. Phys. Rev. Lett. 100, 127002 (2008)

  103. 103.

    , , , & Normal-state transport properties of Bi2+xSr2-yCuO6+δ crystals. Phys. Rev. B 41, 846–849 (1990)

  104. 104.

    , & Effect of Zn impurities on the normal-state Hall angle in single-crystal YBa2Cu3-xZnxO7-δ. Phys. Rev. Lett. 67, 2088–2091 (1991)

  105. 105.

    et al. Temperature dependent scattering rates at the Fermi surface of optimally doped Bi2Sr2CaCu2O8+δ. Phys. Rev. Lett. 85, 828–831 (2000)

  106. 106.

    Quantum Phase Transitions (Cambridge Univ. Press, 1999)An authoritative text covering the fundamentals of quantum phase transitions.

  107. 107.

    Superconductivity: why the temperature is high. Nature 430, 512–513 (2004)

  108. 108.

    , , & Energy and length scales in the superconducting phase diagram for HTSC cuprates. Physica C 235–240, 1821–1822 (1994)

  109. 109.

    et al. Phase competition in trisected superconducting dome. Proc. Natl Acad. Sci. USA 109, 18332–18337 (2012)

  110. 110.

    et al. A quantum critical point at the heart of high temperature superconductivity. Preprint at (2014)

  111. 111.

    , & Singular quasiparticle scattering in the proximity of charge instabilities. Phys. Rev. Lett. 75, 4650–4653 (1995)

  112. 112.

    The large N limit of superconformal field theories and supergravity. Adv. Theor. Math. Phys. 2, 231–252 (1998)

  113. 113.

    , , & Holographic Duality for Condensed Matter Physics (Cambridge Univ. Press, in the press).A comprehensive but accessible text for condensed matter applications of the AdS/CFT correspondence.

  114. 114.

    , & Lectures on holographic non-Fermi liquids and quantum phase transitions. In String Theory and Its Applications, TASI 2010, (eds , & ) 707–816 (World Scientific, 2012)

  115. 115.

    et al. Quantum oscillations in an overdoped high-Tc superconductor. Nature 455, 952–955 (2008)

  116. 116.

    et al. Fermi surface and quasiparticle excitations of overdoped Tl2Ba2CuO6+δ. Phys. Rev. Lett. 95, 077001 (2005)

  117. 117.

    et al. Direct relation between the low-energy spin excitations and superconductivity of overdoped high-Tc superconductors. Phys. Rev. Lett. 92, 217004 (2004)

  118. 118.

    et al. Dispersive spin excitations in highly overdoped cuprates revealed by resonant inelastic x-ray scattering. Phys. Rev. B 88, 020501 (2013)

  119. 119.

    et al. Crossover from coherent to incoherent electronic excitations in the normal state of Bi2Sr2CaCu2O8+δ. Phys. Rev. Lett. 90, 207003 (2003)

  120. 120.

    et al. High-temperature interface superconductivity between metallic and insulating copper oxides. Nature 455, 782–785 (2008)

Download references

Acknowledgements

We thank A. Yazdani for many discussions. S.A.K. was supported by the US DOE, Basic Energy Sciences, Materials Science and Engineering, under Award No. DE-AC02-76SF00515 at Stanford University. M.N. was supported by the Center for Emergent Superconductivity, an Energy Frontier Research Center funded by the US DOE, Basic Energy Sciences, under Award No. DE-AC0298CH1088. J.Z. acknowledges financial support by the Netherlands Organization for Scientific Research/Ministry of Science and Education (NWO/OCW), and a grant from the Templeton foundation: the opinions expressed in this publication are those of the authors and do not necessarily reflect the views of the John Templeton foundation.

Author information

Affiliations

  1. Max Planck Institute for Solid State Research, Heisenbergstrasse 1, D-70569 Stuttgart, Germany

    • B. Keimer
  2. Department of Physics, Stanford University, Stanford, California 94305, USA

    • S. A. Kivelson
  3. Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA

    • M. R. Norman
  4. Department of Physics, University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan

    • S. Uchida
  5. Lorentz Institute for Theoretical Physics, Universiteit Leiden, PO Box 9506, 2300 RA Leiden, The Netherlands

    • J. Zaanen

Authors

  1. Search for B. Keimer in:

  2. Search for S. A. Kivelson in:

  3. Search for M. R. Norman in:

  4. Search for S. Uchida in:

  5. Search for J. Zaanen in:

Contributions

All authors contributed to the text. S.U. prepared the figures.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to J. Zaanen.

About this article

Publication history

Received

Accepted

Published

DOI

https://doi.org/10.1038/nature14165

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.