Letter | Published:

Normal-state nodal electronic structure in underdoped high-Tc copper oxides

Nature volume 511, pages 6164 (03 July 2014) | Download Citation

Abstract

An outstanding problem in the field of high-transition-temperature (high-Tc) superconductivity is the identification of the normal state out of which superconductivity emerges in the mysterious underdoped regime1. The normal state uncomplicated by thermal fluctuations can be studied using applied magnetic fields that are sufficiently strong to suppress long-range superconductivity at low temperatures2,3. Proposals in which the normal ground state is characterized by small Fermi surface pockets that exist in the absence of symmetry breaking1,4,5,6,7,8 have been superseded by models based on the existence of a superlattice that breaks the translational symmetry of the underlying lattice7,8,9,10,11,12,13,14,15. Recently, a charge superlattice model that positions a small electron-like Fermi pocket in the vicinity of the nodes (where the superconducting gap is minimum)8,9,16,17 has been proposed as a replacement for the prevalent superlattice models10,11,12,13,14 that position the Fermi pocket in the vicinity of the pseudogap at the antinodes (where the superconducting gap is maximum)18. Although some ingredients of symmetry breaking have been recently revealed by crystallographic studies, their relevance to the electronic structure remains unresolved19,20,21. Here we report angle-resolved quantum oscillation measurements in the underdoped copper oxide YBa2Cu3O6 + x. These measurements reveal a normal ground state comprising electron-like Fermi surface pockets located in the vicinity of the nodes, and also point to an underlying superlattice structure of low frequency and long wavelength with features in common with the charge order identified recently by complementary spectroscopic techniques14,19,20,21,22.

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.

    , & Doping a Mott insulator: physics of high-temperature superconductivity. Rev. Mod. Phys. 78, 17–85 (2006)

  2. 2.

    et al. Direct measurement of the upper critical field in cuprate superconductors. Nature Commun. 5, 4280 (2014)

  3. 3.

    et al. High field phase diagram of cuprates derived from the Nernst effect. Phys. Rev. Lett. 88, 257003 (2002)

  4. 4.

    , & Phenomenological theory of the pseudogap state. Phys. Rev. B 73, 174501 (2006)

  5. 5.

    et al. The physics behind high-temperature superconducting cuprates: the ‘plain vanilla’ version of RVB. J. Phys. Condens. Matter 16, R755–R769 (2004)

  6. 6.

    et al. Heat capacity through the magnetic-field-induced resistive transition in an underdoped high-temperature superconductor. Nature Phys. 7, 332–335 (2011)

  7. 7.

    et al. Quantum oscillations and the Fermi surface in an underdoped high-Tc superconductor. Nature 447, 565–568 (2007)

  8. 8.

    , & Towards resolution of the Fermi surface in underdoped high-Tc superconductors. Rep. Prog. Phys. 75, 102501 (2012)

  9. 9.

    & Protected nodal electron pocket from multiple-Q ordering in underdoped high temperature superconductors. Phys. Rev. Lett. 106, 226402 (2011)

  10. 10.

    et al. Electron pockets in the Fermi surface of hole-doped high-Tc superconductors. Nature 450, 533–536 (2007)

  11. 11.

    & Fermi pockets and quantum oscillations of the Hall coefficient in high-temperature superconductors. Proc. Natl Acad. Sci. USA 105, 8835–8839 (2008)

  12. 12.

    & Antiphase stripe order as the origin of electron pockets observed in 1/8-hole-doped cuprates. Phys. Rev. B 76, 220503 (2007)

  13. 13.

    , & Fermi-surface reconstruction in a smectic phase of a high-temperature superconductor. Phys. Rev. B 84, 012507 (2011)

  14. 14.

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

  15. 15.

    , , & Quantum oscillations in magnetic-field-induced antiferromagnetic phase of underdoped cuprates: application to ortho-II YBa2Cu3O6.5. Europhys. Lett. 82, 17004 (2008)

  16. 16.

    et al. Quantum oscillations from nodal bilayer magnetic breakdown in the underdoped high temperature superconductor YBa2Cu3O6+x. Phys. Rev. Lett. 108, 196403 (2012)

  17. 17.

    et al. Chemical potential oscillations from nodal Fermi surface pocket in the underdoped high-temperature superconductor YBa2Cu3O6+x. Nature Commun. 2, 471 (2011)

  18. 18.

    et al. In situ doping control of the surface of high-temperature superconductors. Nature Phys. 4, 527–531 (2008)

  19. 19.

    et al. Long-range incommensurate charge fluctuations in (Y,Nd)Ba2Cu3O6+x. Science 337, 821–825 (2012)

  20. 20.

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

  21. 21.

    et al. Thermodynamic phase diagram of static charge order in underdoped YBa2Cu3Oy. Nature Phys. 9, 79–83 (2013)

  22. 22.

    et al. A new collective mode in YBCO observed by time-domain reflectometry. Phys. Rev. B 88, 060508 (2013)

  23. 23.

    , , , & Quasi-two-dimensional Fermi liquid properties of the unconventional superconductor Sr2RuO4. Adv. Phys. 52, 639–725 (2003)

  24. 24.

    , & Checkerboard charge density wave and pseudogap of high-Tc cuprate. Phys. Rev. B 74, 184515 (2006)

  25. 25.

    & Charge order and loop currents in hole-doped cuprates. Preprint at (2014)

  26. 26.

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

  27. 27.

    , , & Angular fluctuations of a multi-component order describe the pseudogap regime of the cuprate superconductors. Science 343, 1336–1339 (2014)

  28. 28.

    , & Pseudogap state near a quantum critical point. Nature Phys. 9, 442–446 (2013)

  29. 29.

    , & Quenched disorder and vestigial nematicity in the pseudo-gap regime of the cuprates. Proc. Natl Acad. Sci. 111, 7980–7985 (2014)

  30. 30.

    et al. New insights into the phase diagram of the copper oxide superconductors from electronic Raman scattering. Rep. Prog. Phys. 76, 022502 (2013)

  31. 31.

    , & Evaluation of CuO2 plane hole doping in YBa2Cu3O6+x single crystals. Phys. Rev. B 73, 180505 (2006)

  32. 32.

    et al. Metal-insulator quantum critical point beneath the high Tc superconducting dome. Proc. Natl Acad. Sci. USA 107, 6175–6179 (2010)

  33. 33.

    , & Proximity detector circuits: an alternative to tunnel diode oscillators for contactless measurements in pulsed magnetic field environments. Rev. Sci. Instrum. 80, 066104 (2009)

  34. 34.

    et al. Vortex lattice melting and Hc2 in underdoped YBa2Cu3Oy. Phys. Rev. B 86, 174501 (2012)

  35. 35.

    , , & Determination of superconducting fluctuations in high-Tc cuprates. J. Phys. Conf. Ser. 449, 012010 (2013)

  36. 36.

    et al. Angle dependence of quantum oscillations in YBa2Cu3O6.59 shows free-spin behaviour of quasiparticles. Nature Phys. 7, 234–238 (2011)

  37. 37.

    On the angle dependence of the magnetoresistance in quasi-two-dimensional organic superconductors. J. Phys. Soc. Jpn 58, 1520–1523 (1989)

  38. 38.

    Magnetic Oscillations in Metals (Cambridge Univ. Press, 1984)

  39. 39.

    & Band Theory and Electronic Properties of Solids (Oxford Univ. Press, 2001)

  40. 40.

    Fermi surfaces of organic superconductors. Int. J. Mod. Phys. B 7, 2707–2741 (1993)

  41. 41.

    High magnetic fields: a tool for studying electronic properties of layered organic metals. Chem. Rev. 104, 5737–5782 (2004)

  42. 42.

    et al. Quantum oscillations in the underdoped cuprate YBa2Cu4O8. Phys. Rev. Lett. 100, 047003 (2008)

  43. 43.

    et al. Quantum oscillations in the underdoped cuprate YBa2Cu4O8. Phys. Rev. Lett. 100, 046004 (2008)

  44. 44.

    et al. Multiple quantum oscillations in the de Haas–van Alphen spectra of the underdoped high-temperature superconductor YBa2Cu3O6.5. Phys. Rev. Lett. 103, 157003 (2009)

  45. 45.

    et al. A multi-component Fermi surface in the vortex state of an underdoped high-Tc superconductor. Nature 454, 200–203 (2008)

  46. 46.

    et al. Magnetic quantum oscillations in YBa2Cu3O6.61 and YBa2Cu3O6.69 in fields of up to 85 T: patching the hole in the roof of the superconducting dome. Phys. Rev. Lett. 104, 086403 (2010)

  47. 47.

    et al. Compensated electron and hole pockets in an underdoped high-Tc superconductor. Phys. Rev. B 81, 214524 (2010)

  48. 48.

    et al. Lifshitz critical point in the cuprate superconductor YBa2Cu3Oy from high-field Hall effect measurements. Phys. Rev. B 83, 054506 (2011)

  49. 49.

    et al. A detailed de Haas–van Alphen effect study of the overdoped cuprate Tl2Ba2CuO6+δ. New J. Phys. 12, 105009/1–29 (2010)

  50. 50.

    et al. Evolution of the Fermi surface of the electron-doped high-temperature superconductor Nd2–xCexCuO4 revealed by Shubnikov–de Haas oscillations. Phys. Rev. Lett. 103, 157002 (2009)

  51. 51.

    Quantum oscillation studies of the Fermi surface of iron-pnictide superconductors. Rep. Prog. Phys. 74, 124507 (2011)

  52. 52.

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

  53. 53.

    et al. Quantum oscillations and the Fermi surface of high-temperature cuprate superconductors. C. R. Phys. 12, 446–460 (2011)

  54. 54.

    Lecture Notes on Electron Correlation and Magnetism (World Scientific, 1999)

  55. 55.

    & The Theory of Quantum Liquids: Normal Fermi Liquids (Addison-Wesley, 1989)

  56. 56.

    & g Factor in metallic zinc. Phys. Rev. 136, A998–A1002 (1964)

  57. 57.

    & The spin flip in the theory of magnetic breakdown: magnetoresistance. Physica B 173, 386–388 (1991)

  58. 58.

    & Multiple quantum oscillation frequencies in YBa2Cu3O6+δ and bilayer splitting. New J. Phys. 12, 105005 (2010)

  59. 59.

    , & Magnetic breakdown of cyclotron orbits in systems with Rashba and Dresselhaus spin-orbit coupling. Phys. Rev. B 78, 115312 (2008)

  60. 60.

    Near doping-independent pocket area from an antinodal Fermi surface instability in underdoped high temperature superconductors. Phys. Rev. Lett. 107, 186408 (2011)

  61. 61.

    & Fermi surface reconstruction from bilayer charge ordering in the underdoped high temperature superconductor YBa2Cu3O6+x. New J. Phys. 14, 095023 (2012)

  62. 62.

    , , & LDA energy bands, low-energy Hamiltonians, t′, t″, t (k) and J. J. Phys. Chem. Solids 56, 1573–1591 (1995)

  63. 63.

    From high temperature superconductivity to quantum spin liquid: progress in strong correlation physics. Rep. Prog. Phys. 71, 012501 (2008)

  64. 64.

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

  65. 65.

    , & Flux-density wave and superconducting instability of the staggered-flux phase. Phys. Rev. B 42, 8690–8693 (1990)

  66. 66.

    & Importance of phase fluctuations in superconductors with small superfluid density. Nature 374, 434–437 (1994)

  67. 67.

    , , , & Evidence for stripe correlations of spins and holes in copper oxide superconductors. Nature 375, 561–563 (1994)

  68. 68.

    &. Morr, D. K. Electronic structure of underdoped cuprates. Phys. Rep. 288, 355–387 (1997)

  69. 69.

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

  70. 70.

    , & Weak pseudogap behavior in the underdoped cuprate superconductors. Phys. Rev. Lett. 80, 3839–3842 (1998)

  71. 71.

    et al. How to detect fluctuating stripes in the high-temperature superconductors. Rev. Mod. Phys. 75, 1201–1241 (2003)

  72. 72.

    & Doped Mott insulators are insulators: hole localization in the cuprates. Phys. Rev. Lett. 95, 196405 (2005)

  73. 73.

    et al. Pseudogap induced by short-range spin correlations in a doped Mott insulator. Phys. Rev. B 73, 165114 (2006)

  74. 74.

    , & Inhomogeneous states with checkerboard order in the tJ model. Phys. Rev. B 73, 060501 (2006)

  75. 75.

    et al. Towards a complete theory of high Tc. Nature Phys. 2, 138–143 (2006)

  76. 76.

    , & Superconductivity without phonons. Nature 450, 1177–1183 (2007)

  77. 77.

    , , & Time-reversal symmetry breaking by a (d+id) density-wave state in underdoped cuprate superconductors. Phys. Rev. Lett. 100, 217004 (2008)

  78. 78.

    & Hidden Fermi liquid: self-consistent theory for the normal state of high-Tc superconductors. Phys. Rev. Lett. 106, 097002 (2009)

  79. 79.

    , , & Striped superconductors: how the cuprates intertwine spin, charge and superconducting orders. New J. Phys. 11, 115004 (2009)

  80. 80.

    & Pseudogap in underdoped cuprates and spin-density-wave fluctuations. Phys. Rev. B 81, 174536 (2010)

  81. 81.

    Magnetic properties of lightly doped antiferromagnetic YBa2Cu3Oy. Phys. Rev. B 84, 094532 (2011)

  82. 82.

    , & A phenomenological theory of the anomalous pseudogap phase in underdoped cuprates. Rep. Prog. Phys. 75, 016502 (2012)

  83. 83.

    A common thread: the pairing interaction for unconventional superconductors. Rev. Mod. Phys. 84, 1383 (2012)

  84. 84.

    & Bond order in two-dimensional metals with antiferromagnetic exchange interactions. Phys. Rev. Lett. 111, 027202 (2013)

  85. 85.

    & Superconductivity at the onset of the spin-density-wave order in a metal. Phys. Rev. Lett. 110, 127001 (2013)

  86. 86.

    Strongly correlated superconductivity. In Autumn School on Correlated Electrons: Emergent Phenomena in Correlated Matter (September 23–27, 2013, Forschungszentrum Julich, Germany) Preprint at (2013)

  87. 87.

    , , , & Kerr effect as evidence of gyrotropic order in the cuprates. Phys. Rev. B 87, 115116 (2013)

  88. 88.

    , & Superconductivity and the pseudogap in the two-dimensional Hubbard model. Phys. Rev. Lett. 110, 216405 (2013)

  89. 89.

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

  90. 90.

    & Mean field theory of competing orders in metals with antiferromagnetic exchange interactions. Phys. Rev. B 89, 075129 (2014)

  91. 91.

    Hartree-Fock computation of the high-Tc cuprate phase diagram. Phys. Rev. B 89, 035134 (2014)

  92. 92.

    , , & Cascade of phase transitions in the vicinity of a quantum critical point. Preprint at (2013)

  93. 93.

    & de Haas-van alphen effect in canonical and grand canonical multiband fermi liquid. Phys. Rev. Lett. 76, 1308–1311 (1996)

  94. 94.

    & Band-structure calculations of Fermi-surface pockets in ortho-II YBa2Cu3O6.5. Phys. Rev. B 76, 140508 (2007)

  95. 95.

    , & Theory of Fermi-surface pockets and correlation effects in underdoped YBa2Cu3O6.5. Phys. Rev. B 77, 060504 (2008)

  96. 96.

    Quantum oscillations in the mixed state of d-wave superconductors. Phys. Rev. B 78, 020502 (2008)

  97. 97.

    Magneto-oscillations in underdoped cuprates. Phys. Rev. B 79, 085110 (2009)

  98. 98.

    & Synthesis of the phenomenology of the underdoped cuprates. Phys. Rev. B 79, 245116 (2009)

  99. 99.

    , , & Quantum oscillations from Fermi arcs. Nature Phys. 6, 44–49 (2010)

  100. 100.

    , & &. Cohen, M. L. Fermi surfaces and quantum oscillations in the underdoped high-Tc superconductors YBa2Cu3O6.5 and YBa2Cu4O8. Phys. Rev. B 84, 014518 (2011)

  101. 101.

    Geometric interpretation of the weak-field Hall conductivity in two-dimensional metals with arbitrary Fermi surface. Phys. Rev. B 43, 193–201 (1991)

  102. 102.

    Saturation Hall constant of semiconductors. Phys. Rev. 99, 1799–1807 (1955)

  103. 103.

    Principles of the Theory of Solids (Cambridge Univ. Press, 1979)

  104. 104.

    & Quantitative theory for the quantum interference effect in the transverse magnetoresistance of pure magnesium. J. Low Temp. Phys. 26, 763–817 (1977)

  105. 105.

    et al. Magnetic breakdown and quantum interference in the quasi-two-dimensional superconductor κ – (BEDT – TTF)2Cu(NCS)2 in high magnetic fields. J. Phys. Condens. Matter 8, 5415–5435 (1996)

  106. 106.

    & Electrodynamics of high-Tc superconductors. Rev. Mod. Phys. 77, 721–779 (2005)

  107. 107.

    , & Connecting high-field quantum oscillations to the pseudogap in the underdoped cuprates. Preprint at (2014)

Download references

Acknowledgements

S.E.S. acknowledges support from the Royal Society, King’s College Cambridge, the Winton Programme for the Physics of Sustainability, and the European Research Council under the European Union’s Seventh Framework Programme (grant number FP/2007-2013)/ERC Grant Agreement number 337425-SUPERCONDUCTINGMOTT. N.H. and F.F.B. acknowledge support for high-magnetic-field experiments from the US Department of Energy, Office of Science, BES-MSE ‘Science of 100 Tesla’ programme. G.G.L. acknowledges support from Engineering and Physical Sciences Research Council (EPSRC) grant EP/K012894/1. P.A.G. is supported by the EPSRC and thanks the University of Oxford for the provision of a Visiting Lectureship. R.L., D.A.B. and W.N.H. acknowledge support from the Canadian Institute for Advanced Research, and the Natural Science and Engineering Research Council. A portion of this work was performed at the National High Magnetic Field Laboratory, which is supported by NSF co-operative agreement number DMR-0654118, the state of Florida, and the DOE. We acknowledge discussions with many colleagues, including H. Alloul, C. Bergemann, A. Carrington, S. Chakravarty, A. Chubukov, E. M. Forgan, S. R. Julian, B. Keimer, S. A. Kivelson, R. B. Laughlin, M. Le Tacon, L. Taillefer, D.-H. Lee, P. A. Lee, P. B. Littlewood, A. P. Mackenzie, M. R. Norman, C. Pépin, C. Proust, M. Randeria, S. Sachdev, A. Sacuto, T. Senthil, J. P. Sethna, J. Tranquada and C. M. Varma. We are grateful for the experimental support provided by the ‘100 T’ team, including J. B. Betts, Y. Coulter, M. Gordon, C. H. Mielke, A. Parish, D. Rickel and D. Roybal.

Author information

Affiliations

  1. Cavendish Laboratory, Cambridge University, JJ Thomson Avenue, Cambridge CB3 OHE, UK

    • Suchitra E. Sebastian
    •  & G. G. Lonzarich
  2. National High Magnetic Field Laboratory, Los Alamos National Laboratory (LANL), Los Alamos, New Mexico 87504, USA

    • N. Harrison
    • , F. F. Balakirev
    •  & M. M. Altarawneh
  3. Department of Physics, Mu’tah University, Mu’tah, Karak 61710, Jordan

    • M. M. Altarawneh
  4. Department of Physics, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, UK

    • P. A. Goddard
  5. Department of Physics and Astronomy, University of British Columbia, Vancouver V6T 1Z4, Canada

    • Ruixing Liang
    • , D. A. Bonn
    •  & W. N. Hardy
  6. Canadian Institute for Advanced Research, Quantum Materials Program, Toronto M5G 1Z8, Canada

    • Ruixing Liang
    • , D. A. Bonn
    •  & W. N. Hardy

Authors

  1. Search for Suchitra E. Sebastian in:

  2. Search for N. Harrison in:

  3. Search for F. F. Balakirev in:

  4. Search for M. M. Altarawneh in:

  5. Search for P. A. Goddard in:

  6. Search for Ruixing Liang in:

  7. Search for D. A. Bonn in:

  8. Search for W. N. Hardy in:

  9. Search for G. G. Lonzarich in:

Contributions

S.E.S., N.H., F.F.B., M.M.A. and P.A.G. performed high magnetic field measurements. R.L., D.A.B. and W.N.H. prepared single crystals. S.E.S., N.H. and G.G.L. analysed data and wrote the paper.

Competing interests

The authors declare no competing financial interests.

Corresponding authors

Correspondence to Suchitra E. Sebastian or N. Harrison.

Extended data

About this article

Publication history

Received

Accepted

Published

DOI

https://doi.org/10.1038/nature13326

Further reading

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.