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Energy gaps in high-transition-temperature cuprate superconductors

Nature Physics volume 10, pages 483–495 (2014)Cite this article

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Abstract

The spectral energy gap is an important signature that defines states of quantum matter: insulators, density waves and superconductors have very different gap structures. The momentum-resolved nature of angle-resolved photoemission spectroscopy (ARPES) makes it a powerful tool to characterize spectral gaps. ARPES has been instrumental in establishing the anisotropic d-wave structure of the superconducting gap in high-transition-temperature (Tc) cuprates, which is different from the conventional isotropic s-wave superconducting gap. Shortly afterwards, ARPES demonstrated that an anomalous gap above Tc, often termed the pseudogap, follows a similar anisotropy. The nature of this poorly understood pseudogap and its relationship with superconductivity has since become the focal point of research in the field. To address this issue, the momentum, temperature, doping and materials dependence of spectral gaps have been extensively examined with significantly improved instrumentation and carefully matched experiments in recent years. This article overviews the current understanding and unresolved issues of the basic phenomenology of gap hierarchy. We show how ARPES has been sensitive to phase transitions, has distinguished between orders having distinct broken electronic symmetries, and has uncovered rich momentum- and temperature-dependent fingerprints reflecting an intertwined and competing relationship between the ordered states and superconductivity that results in multiple phenomenologically distinct ground states inside the superconducting dome. These results provide us with microscopic insights into the cuprate phase diagram.

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Figure 1: High-Tc cuprate superconductors.
Figure 2: d-wave superconducting gap symmetry in cuprates witnessed by ARPES and the improvement of ARPES data quality.
Figure 3: Nodal–antinodal dichotomy in Bi2212.
Figure 4: Dichotomy between the antinodal and nodal regions in Bi2201.
Figure 5: Broken-symmetry nature of the pseudogap in Bi2201.
Figure 6: Proposed phase diagram of Bi2212.

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References

  1. Imada, M., Fujimori, A. & Tokura, Y. Metal–insulator transitions. Rev. Mod. Phys. 70, 1039–1263 (1998).

    Article  ADS  Google Scholar 

  2. Bednorz, J. G. & Muller, K. A. Possible high-Tc superconductivity in the Ba–La–Cu–O system. Z. Phys. B 64, 189–193 (1986).

    Article  ADS  Google Scholar 

  3. Wu, M. K. et al. 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 

  4. Bardeen, J., Cooper, L. N. & Schrieffer, J. R. Theory of superconductivity. Phys. Rev. 108, 1175–1204 (1957).

    Article  ADS  MathSciNet  MATH  Google Scholar 

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

    Article  ADS  Google Scholar 

  6. Shen, Z. X. et al. Anomalously large gap anisotropy in the A–B plane of Bi2Sr2CaCu2O8 + δ . Phys. Rev. Lett. 70, 1553–1556 (1993).

    Article  ADS  Google Scholar 

  7. Timusk, T. & Statt, B. The pseudogap in high-temperature superconductors: An experimental survey. Rep. Prog. Phys. 62, 61–122 (1999).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  9. Marshall, D. S. et al. Unconventional electronic structure evolution with hole doping in Bi2Sr2CaCu2O8 + δ: Angle-resolved photoemission results. Phys. Rev. Lett. 76, 4841–4844 (1996).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  12. Hashimoto, M. et al. Particle–hole symmetry breaking in the pseudogap state of Bi2201. Nature Phys. 6, 414–418 (2010).

    Article  ADS  Google Scholar 

  13. He, R. H. et al. From a single-band metal to a high-temperature superconductor via two thermal phase transitions. Science 331, 1579–1583 (2011).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  15. Damascelli, A., Hussain, Z. & Shen, Z. X. Angle-resolved photoemission studies of the cuprate superconductors. Rev. Mod. Phys. 75, 473–541 (2003).

    Article  ADS  Google Scholar 

  16. Vishik, I. M. et al. Doping-dependent nodal Fermi velocity of the high-temperature superconductor Bi2Sr2CaCu2O8 + δ revealed using high-resolution angle-resolved photoemission spectroscopy. Phys. Rev. Lett. 104, 207002 (2010).

    Article  ADS  Google Scholar 

  17. Johnston, S. et al. Evidence for the importance of extended Coulomb interactions and forward scattering in cuprate superconductors. Phys. Rev. Lett. 108, 166404 (2012).

    Article  ADS  Google Scholar 

  18. Kondo, T. et al. Anomalous doping variation of the nodal low-energy feature of superconducting (Bi, Pb)2(Sr, La)2CuO6 + δ crystals revealed by laser-based angle-resolved photoemission spectroscopy. Phys. Rev. Lett. 110, 217006 (2013).

    Article  ADS  Google Scholar 

  19. Kondo, T. et al. Observation of quasiparticles for phase incoherent d-wave pairing in Bi2212. Preprint at http://arXiv.org/abs/1404.0911 (2014).

  20. Okawa, M. et al. Superconducting electronic state in optimally doped YBa2Cu3O7 − δ observed with laser-excited angle-resolved photoemission spectroscopy. Phys. Rev. B 79, 144528 (2009).

    Article  ADS  Google Scholar 

  21. Ishizaka, K. et al. Doping-dependence of nodal quasiparticle properties in high-Tc cuprates studied by laser-excited angle-resolved photoemission spectroscopy. Phys. Rev. B 77, 064522 (2008).

    Article  ADS  Google Scholar 

  22. Meng, J. Q. et al. Monotonic d-wave superconducting gap of the optimally doped Bi2Sr1.6La0.4CuO6 superconductor by laser-based angle-resolved photoemission spectroscopy. Phys. Rev. B 79, 024514 (2009).

    Article  ADS  Google Scholar 

  23. Peng, Y. Y. et al. Disappearance of nodal gap across the insulator–superconductor transition in a copper-oxide superconductor. Nature Commun. 4, 2459 (2013).

    Article  ADS  Google Scholar 

  24. Hardy, W. N., Bonn, D. A., Morgan, D. C., Liang, R. X. & Zhang, K. Precision-measurements of the temperature-dependence of lambda in YBa2Cu3O6.95—Strong evidence for nodes in the gap function. Phys. Rev. Lett. 70, 3999–4002 (1993).

    Article  ADS  Google Scholar 

  25. Devereaux, T. P. & Hackl, R. Inelastic light scattering from correlated electrons. Rev. Mod. Phys. 79, 175–233 (2007).

    Article  ADS  Google Scholar 

  26. Van Harlingen, D. J. Phase-sensitive tests of the symmetry of the pairing state in the high-temperature superconductors—Evidence for dx2 − y2 symmetry. Rev. Mod. Phys. 67, 515–535 (1995).

    Article  ADS  Google Scholar 

  27. Norman, M. R., Randeria, M., Ding, H. & Campuzano, J. C. Phenomenology of the low-energy spectral function in high-Tc superconductors. Phys. Rev. B 57, R11093 (1998).

    Article  ADS  Google Scholar 

  28. Lee, W. S. et al. Abrupt onset of a second energy gap at the superconducting transition of underdoped Bi2212. Nature 450, 81–84 (2007).

    Article  ADS  Google Scholar 

  29. Loeser, A. G. et al. Temperature and doping dependence of the Bi–Sr–Ca–Cu–O electronic structure and fluctuation effects. Phys. Rev. B 56, 14185–14189 (1997).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  31. Campuzano, J. C. et al. Electronic spectra and their relation to the (π, π) collective mode in high-Tc superconductors. Phys. Rev. Lett. 83, 3709–3712 (1999).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  34. Ding, H. et al. Coherent quasiparticle weight and its connection to high-Tc superconductivity from angle-resolved photoemission. Phys. Rev. Lett. 87, 227001 (2001).

    Article  ADS  Google Scholar 

  35. Feng, D. L. et al. Electronic structure of the trilayer cuprate superconductor Bi2Sr2Ca2Cu3O10 + δ . Phys. Rev. Lett. 88, 107001 (2002).

    Article  ADS  Google Scholar 

  36. Wei, J. et al. Superconducting coherence peak in the electronic excitations of a single-layer Bi2Sr1.6La0.4CuO6 + δ cuprate superconductor. Phys. Rev. Lett. 101, 097005 (2008).

    Article  ADS  Google Scholar 

  37. Kanigel, A. et al. Evolution of the pseudogap from Fermi arcs to the nodal liquid. Nature Phys. 2, 447–451 (2006).

    Article  ADS  Google Scholar 

  38. Terashima, K. et al. Anomalous momentum dependence of the superconducting coherence peak and its relation to the pseudogap of La1.85Sr0.15CuO4 . Phys. Rev. Lett. 99, 017003 (2007).

    Article  ADS  Google Scholar 

  39. Kanigel, A. et al. Protected nodes and the collapse of Fermi arcs in high-Tc cuprate superconductors. Phys. Rev. Lett. 99, 157001 (2007).

    Article  ADS  Google Scholar 

  40. Kondo, T., Takeuchi, T., Kaminski, A., Tsuda, S. & Shin, S. Evidence for two energy scales in the superconducting state of optimally doped (Bi, Pb)2(Sr, La)2CuO6 + δ . Phys. Rev. Lett. 98, 267004 (2007).

    Article  ADS  Google Scholar 

  41. Ma, J. H. et al. Coexistence of competing orders with two energy gaps in real and momentum space in the high temperature superconductor Bi2Sr2 − xLaxCuO6 + δ . Phys. Rev. Lett. 101, 207002 (2008).

    Article  ADS  Google Scholar 

  42. Okada, Y., Takeuchi, T., Baba, T., Shin, S. & Ikuta, H. Origin of the anomalously strong influence of out-of-plane disorder on high-Tc superconductivity. J. Phys. Soc. Jpn 77, 074714 (2008).

    Article  ADS  Google Scholar 

  43. Shi, M. et al. Coherent d-wave superconducting gap in underdoped La2 − xSrxCuO4 by angle-resolved photoemission spectroscopy. Phys. Rev. Lett. 101, 047002 (2008).

    Article  ADS  Google Scholar 

  44. Kanigel, A. et al. Evidence for pairing above the transition temperature of cuprate superconductors from the electronic dispersion in the pseudogap phase. Phys. Rev. Lett. 101, 137002 (2008).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  46. Yoshida, T. et al. Universal versus material-dependent two-gap behaviors of the high-Tc cuprate superconductors: Angle-resolved photoemission study of La2 − xSrxCuO4 . Phys. Rev. Lett. 103, 037004 (2009).

    Article  ADS  Google Scholar 

  47. Kondo, T., Khasanov, R., Takeuchi, T., Schmalian, J. & Kaminski, A. Competition between the pseudogap and superconductivity in the high-Tc copper oxides. Nature 457, 296–300 (2009).

    Article  ADS  Google Scholar 

  48. He, R. H. et al. Energy gaps in the failed high-Tc superconductor La1.875Ba0.125CuO4 . Nature Phys. 5, 119–123 (2009).

    Article  ADS  Google Scholar 

  49. Shi, M. et al. Spectroscopic evidence for preformed Cooper pairs in the pseudogap phase of cuprates. Europhys. Lett. 88, 27008 (2009).

    Article  ADS  Google Scholar 

  50. Nakayama, K. et al. Evolution of a pairing-induced pseudogap from the superconducting gap of (Bi, Pb)2Sr2CuO6 . Phys. Rev. Lett. 102, 227006 (2009).

    Article  ADS  Google Scholar 

  51. Meng, J. Q. et al. Coexistence of Fermi arcs and Fermi pockets in a high-Tc copper oxide superconductor. Nature 462, 335–338 (2009).

    Article  ADS  Google Scholar 

  52. Vishik, I. M. et al. ARPES studies of cuprate fermiology: Superconductivity, pseudogap and quasiparticle dynamics. New J. Phys. 12, 105008 (2010).

    Article  ADS  Google Scholar 

  53. Yoshida, T., Hashimoto, M., Vishik, I. M., Shen, Z. X. & Fujimori, A. Pseudogap, superconducting gap, and Fermi arc in high-Tc cuprates revealed by angle-resolved photoemission spectroscopy. J. Phys. Soc. Jpn 81, 011006 (2012).

    Article  ADS  Google Scholar 

  54. Hashimoto, M. et al. Reaffirming the d x2 − y2 superconducting gap using the autocorrelation angle-resolved photoemission spectroscopy of Bi1.5Pb0.55Sr1.6La0.4CuO6 + δ . Phys. Rev. Lett. 106, 167003 (2011).

    Article  ADS  Google Scholar 

  55. Okada, Y. et al. Three energy scales characterizing the competing pseudogap state, the incoherent, and the coherent superconducting state in high-Tc cuprates. Phys. Rev. B 83, 104502 (2011).

    Article  ADS  Google Scholar 

  56. Nakayama, K. et al. Two pseudogaps with different energy scales at the antinode of the high-temperature Bi2Sr2CuO6 superconductor using angle-resolved photoemission spectroscopy. Phys. Rev. B 83, 224509 (2011).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  58. Kondo, T. et al. Disentangling Cooper-pair formation above the transition temperature from the pseudogap state in the cuprates. Nature Phys. 7, 21–25 (2011).

    Article  ADS  Google Scholar 

  59. Yang, H. B. et al. Reconstructed Fermi surface of underdoped Bi2Sr2CaCu2O8 + δ cuprate superconductors. Phys. Rev. Lett. 107, 047003 (2011).

    Article  ADS  Google Scholar 

  60. Ideta, S-i. et al. Energy scale directly related to superconductivity in high-Tc cuprates: Universality from the temperature-dependent angle-resolved photoemission of Bi2Sr2Ca2Cu3O10 + δ . Phys. Rev. B 85, 104515 (2012).

    Article  ADS  Google Scholar 

  61. Anzai, H. et al. Relation between the nodal and antinodal gap and critical temperature in superconducting Bi2212. Nature Commun. 4, 1815 (2013).

    Article  ADS  Google Scholar 

  62. Zhao, J. et al. Universal features in the photoemission spectroscopy of high temperature superconductors. Proc. Natl Acad. Sci. USA 110, 17774–17777 (2013).

    Article  ADS  Google Scholar 

  63. Kondo, T. et al. Formation of gapless Fermi arcs and fingerprints of order in the pseudogap state of cuprate superconductors. Phys. Rev. Lett. 111, 157003 (2013).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  66. Parham, S. et al. Pair breaking caused by magnetic impurities in the high-temperature superconductor Bi2.1Sr1.9Ca(Cu1 − xFex)2Oy . Phys. Rev. B 87, 104501 (2013).

    Article  ADS  Google Scholar 

  67. Reber, T. J. et al. Prepairing and the ‘filling’ gap in the cuprates from the tomographic density of states. Phys. Rev. B 87, 060506 (2013).

    Article  ADS  Google Scholar 

  68. Feng, D. L. et al. Bilayer splitting in the electronic structure of heavily overdoped Bi2Sr2CaCu2O8 + δ . Phys. Rev. Lett. 86, 5550–5553 (2001).

    Article  ADS  Google Scholar 

  69. Baumberger, F., Greber, T. & Osterwalder, J. Fermi surfaces of the two-dimensional surface states on vicinal Cu(111). Phys. Rev. B 64, 195411 (2001).

    Article  ADS  Google Scholar 

  70. Tanaka, K. et al. Distinct Fermi-momentum-dependent energy gaps in deeply underdoped Bi2212. Science 314, 1910–1913 (2006).

    Article  ADS  Google Scholar 

  71. Mesot, J. et al. Superconducting gap anisotropy and quasiparticle interactions: A doping dependent photoemission study. Phys. Rev. Lett. 83, 840–843 (1999).

    Article  ADS  Google Scholar 

  72. Nakayama, K. et al. Doping dependence of the gap anisotropy of the high-temperature YBa2Cu3O7 − δ superconductor. Phys. Rev. B 79, 140503 (2009).

    Article  ADS  Google Scholar 

  73. Hashimoto, M. et al. Effects of out-of-plane disorder on the nodal quasiparticle and superconducting gap in single-layer Bi2Sr1.6L0.4CuO6 + δ (L = La, Nd, Gd). Phys. Rev. B 79, 144517 (2009).

    Article  ADS  Google Scholar 

  74. Ideta, S. et al. Enhanced superconducting gaps in the trilayer high-temperature Bi2Sr2Ca2Cu3O10 + δ cuprate superconductor. Phys. Rev. Lett. 104, 227001 (2010).

    Article  ADS  Google Scholar 

  75. Hashimoto, M. et al. Superconductivity distorted by the coexisting pseudogap in the antinodal region of Bi1.5Pb0.55Sr1.6La0.4CuO6 + δ: A photon-energy-dependent angle-resolved photoemission study. Phys. Rev. B 86, 094504 (2012).

    Article  ADS  Google Scholar 

  76. Yoshida, T. et al. Coexisting pseudo-gap and superconducting gap in the high-Tc superconductor La2 − xSrxCuO4. Preprint at http://arXiv.org/abs/1208.2903 (2012).

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

    Article  ADS  Google Scholar 

  78. Hashimoto, M. et al. Direct spectroscopic evidence for phase competition between the pseudogap and superconductivity in Bi2Sr2CaCu2O8 + δ. Preprint at http://arXiv.org/abs/1405.5199 (2014).

  79. Ando, Y., Segawa, K., Komiya, S. & Lavrov, A. N. Electrical resistivity anisotropy from self-organized one dimensionality in high-temperature superconductors. Phys. Rev. Lett. 88, 137005 (2002).

    Article  ADS  Google Scholar 

  80. Kaminski, A. et al. Spontaneous breaking of time-reversal symmetry in the pseudogap state of a high-Tc superconductor. Nature 416, 610–613 (2002).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  82. Zheng, G. Q., Kuhns, P. L., Reyes, A. P., Liang, B. & Lin, C. T. Critical point and the nature of the pseudogap of single-layered copper-oxide Bi2Sr2 − xLaxCuO6 + δ superconductors. Phys. Rev. Lett. 94, 047006 (2005).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  84. Kohsaka, Y. et al. An intrinsic bond-centered electronic glass with unidirectional domains in underdoped cuprates. Science 315, 1380–1385 (2007).

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

  86. Li, Y. et al. Unusual magnetic order in the pseudogap region of the superconductor HgBa2CuO4 + δ . Nature 455, 372–375 (2008).

    Article  ADS  Google Scholar 

  87. Mook, H. A., Sidis, Y., Fauqué, B., Balédent, V. & Bourges, P. Observation of magnetic order in a superconducting YBa2Cu3O6.6 single crystal using polarized neutron scattering. Phys. Rev. B 78, 020506 (2008).

    Article  ADS  Google Scholar 

  88. Xia, J. 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).

    Article  ADS  Google Scholar 

  89. Yu, L. et al. Evidence for two separate energy gaps in underdoped high-temperature cuprate superconductors from broadband infrared ellipsometry. Phys. Rev. Lett. 100, 177004 (2008).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  93. Taillefer, L. Scattering and pairing in cuprate superconductors. Annu. Rev. Cond. Matter Phys. 1, 51–70 (2010).

    Article  ADS  Google Scholar 

  94. Shekhter, A. et al. Bounding the pseudogap with a line of phase transitions in YBa2Cu3O6 + δ . Nature 498, 75–77 (2013).

    Article  ADS  Google Scholar 

  95. Tranquada, J. M., Sternlieb, B. J., Axe, J. D., Nakamura, Y. & Uchida, S. Evidence for stripe correlations of spins and holes in copper-oxide superconductors. Nature 375, 561–563 (1995).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  97. Hoffman, J. E. et al. A four unit cell periodic pattern of quasi-particle states surrounding vortex cores in Bi2Sr2CaCu2O8 + δ . Science 295, 466–469 (2002).

    Article  ADS  Google Scholar 

  98. Howald, C., Eisaki, H., Kaneko, N. & Kapitulnik, A. Coexistence of periodic modulation of quasiparticle states and superconductivity in Bi2Sr2CaCu2O8 + δ . Proc. Natl Acad. Sci. USA 100, 9705–9709 (2003).

    Article  ADS  Google Scholar 

  99. Shen, K. M. et al. Nodal quasiparticles and antinodal charge ordering in Ca2 − xNaxCuO2Cl2 . Science 307, 901–904 (2005).

    Article  ADS  Google Scholar 

  100. Wise, W. D. et al. Charge-density-wave origin of cuprate checkerboard visualized by scanning tunnelling microscopy. Nature Phys. 4, 696–699 (2008).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  102. Hashimoto, M. et al. Direct observation of bulk charge modulations in optimally-doped Bi1.5Pb0.6Sr1.54CaCu2O8 + δ. Preprint at http://arXiv.org/abs/1403.0061 (2014).

  103. Abbamonte, P. et al. Spatially modulated ‘Mottness’ in La2 − xBaxCuO4 . Nature Phys. 1, 155–158 (2005).

    Article  ADS  Google Scholar 

  104. Hucker, M. et al. Stripe order in superconducting La2 − xBaxCuO4 (0.095 < = x < = 0.155). Phys. Rev. B 83, 104506 (2011).

    Article  ADS  Google Scholar 

  105. Wilkins, S. B. et al. Comparison of stripe modulations in La1.875Ba0.125CuO4 and La1.48Nd0.4Sr0.12CuO4 . Phys. Rev. B 84, 195101 (2011).

    Article  ADS  Google Scholar 

  106. Dean, M. P. M. et al. Magnetic excitations in stripe-ordered La1.875Ba0.125CuO4 studied using resonant inelastic x-ray scattering. Phys. Rev. B 88, 020403 (2013).

    Article  ADS  Google Scholar 

  107. Thampy, V. et al. Comparison of charge modulations in La1.875Ba0.125CuO4 and YBa2Cu3O6.6 . Phys. Rev. B 88, 024505 (2013).

    Article  ADS  Google Scholar 

  108. Fink, J. et al. Phase diagram of charge order in La1.8 − xEu0.2SrxCuO4 from resonant soft x-ray diffraction. Phys. Rev. B 83, 092503 (2011).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  111. Achkar, A. J. et al. Distinct charge orders in the planes and chains of ortho-III-ordered YBa2Cu3O6 + δ superconductors identified by resonant elastic x-ray scattering. Phys. Rev. Lett. 109, 167001 (2012).

    Article  ADS  Google Scholar 

  112. Blackburn, E. et al. X-ray diffraction observations of a charge-density-wave order in superconducting Ortho-II YBa2Cu3O6.54 single crystals in zero magnetic field. Phys. Rev. Lett. 110, 137004 (2013).

    Article  ADS  Google Scholar 

  113. Le Tacon, M. 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).

    Article  ADS  Google Scholar 

  114. Demsar, J., Podobnik, B., Kabanov, V. V., Wolf, T. & Mihailovic, D. Superconducting gap Δc, the pseudogap Δp, and pair fluctuations above Tc in overdoped Y1 − xCaxBa2Cu3O7 − δ from femtosecond time-domain spectroscopy. Phys. Rev. Lett. 82, 4918–4921 (1999).

    Article  ADS  Google Scholar 

  115. Kaindl, R. A. et al. Ultrafast mid-infrared response of YRa2Cu3O7 − δ . Science 287, 470–473 (2000).

    Article  ADS  Google Scholar 

  116. Gedik, N. et al. Single-quasiparticle stability and quasiparticle-pair decay in YBa2Cu3O6.5 . Phys. Rev. B 70, 014504 (2004).

    Article  ADS  Google Scholar 

  117. Chia, E. E. M. et al. Observation of competing order in a high-Tc superconductor using femtosecond optical pulses. Phys. Rev. Lett. 99, 147008 (2007).

    Article  ADS  Google Scholar 

  118. Liu, Y. H. et al. Direct observation of the coexistence of the pseudogap and superconducting quasiparticles in Bi2Sr2CaCu2O8 + y by time-resolved optical spectroscopy. Phys. Rev. Lett. 101, 137003 (2008).

    Article  ADS  Google Scholar 

  119. Chakravarty, S., Laughlin, R. B., Morr, D. K. & Nayak, C. Hidden order in the cuprates. Phys. Rev. B 63, 094503 (2001).

    Article  ADS  Google Scholar 

  120. Corson, J., Mallozzi, R., Orenstein, J., Eckstein, J. N. & Bozovic, I. Vanishing of phase coherence in underdoped Bi2Sr2CaCu2O8 + δ . Nature 398, 221–223 (1999).

    Article  ADS  Google Scholar 

  121. Xu, Z. A., Ong, N. P., Wang, Y., Kakeshita, T. & Uchida, S. Vortex-like excitations and the onset of superconducting phase fluctuation in underdoped La2 − xSrxCuO4 . Nature 406, 486–488 (2000).

    Article  ADS  Google Scholar 

  122. Wang, Y., Li, L. & Ong, N. P. Nernst effect in high-Tc superconductors. Phys. Rev. B 73, 024510 (2006).

    Article  ADS  Google Scholar 

  123. Kitano, H., Ohashi, T., Maeda, A. & Tsukada, I. Critical microwave-conductivity fluctuations across the phase diagram of superconducting La2 − xSrxCuO4 thin films. Phys. Rev. B 73, 092504 (2006).

    Article  ADS  Google Scholar 

  124. Grbic, M. S. et al. Microwave measurements of the in-plane and c-axis conductivity in HgBa2CuO4 + δ: Discriminating between superconducting fluctuations and pseudogap effects. Phys. Rev. B 80, 094511 (2009).

    Article  ADS  Google Scholar 

  125. Bilbro, L. S. et al. Temporal correlations of superconductivity above the transition temperature in La2 − xSrxCuO4 probed by terahertz spectroscopy. Nature Phys. 7, 298–302 (2011).

    Article  ADS  Google Scholar 

  126. Grbic, M. S. et al. Temperature range of superconducting fluctuations above Tc in YBa2Cu3O7 − δ single crystals. Phys. Rev. B 83, 144508 (2011).

    Article  ADS  Google Scholar 

  127. Tallon, J. L., Loram, J. W., Cooper, J. R., Panagopoulos, C. & Bernhard, C. Superfluid density in cuprate high-Tc superconductors: A new paradigm. Phys. Rev. B 68, 180501 (2003).

    Article  ADS  Google Scholar 

  128. Boyer, M. C. et al. Imaging the two gaps of the high-temperature superconductor Bi2Sr2CuO6 + x . Nature Phys. 3, 802–806 (2007).

    Article  ADS  Google Scholar 

  129. Pushp, A. et al. Extending universal nodal excitations optimizes superconductivity in Bi2Sr2CaCu2O8 + δ . Science 324, 1689–1693 (2009).

    Article  ADS  Google Scholar 

  130. Tallon, J. L. & Loram, J. W. The doping dependence of T∗—What is the real high-Tc phase diagram? Physica C 349, 53–68 (2001).

    Article  ADS  Google Scholar 

  131. Anukool, W., Barakat, S., Panagopoulos, C. & Cooper, J. R. Effect of hole doping on the London penetration depth in Bi2.15Sr1.85CaCu2O8 + δ and Bi2.1Sr1.9Ca0.85Y0.15Cu2O8 + δ . Phys. Rev. B 80, 024516 (2009).

    Article  ADS  Google Scholar 

  132. Shen, K. M. et al. Fully gapped single-particle excitations in lightly doped cuprates. Phys. Rev. B 69, 054503 (2004).

    Article  ADS  Google Scholar 

  133. Hashimoto, M. et al. Doping evolution of the electronic structure in the single-layer cuprate Bi2Sr2 − xLaxCuO6 + δ: Comparison with other single-layer cuprates. Phys. Rev. B 77, 094516 (2008).

    Article  ADS  Google Scholar 

  134. Tanaka, K. et al. Evolution of electronic structure from insulator to superconductor in Bi2Sr2 − xLax(Ca, Y)Cu2O8 + δ . Phys. Rev. B 81, 125115 (2010).

    Article  ADS  Google Scholar 

  135. Haug, D. et al. Neutron scattering study of the magnetic phase diagram of underdoped YBa2Cu3O6 + x . New J. Phys. 12, 105006 (2010).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  138. Drachuck, G. et al. Comprehensive study of the spin-charge interplay in antiferromagnetic La2 − xSrxCuO4 . Nature Commun. 5, 3390 (2014).

    Article  ADS  Google Scholar 

  139. Razzoli, E. et al. Evolution from a nodeless gap to d x2 − y2-wave in underdoped La2 − xSrxCuO4 . Phys. Rev. Lett. 110, 047004 (2013).

    Article  ADS  Google Scholar 

  140. Lu, Y-M., Xiang, T. & Lee, D-H. Can deeply underdoped superconducting cuprates be topological superconductors? Preprint at http://arXiv.org/abs/1311.5892 (2013).

  141. Das, T. Nodeless superconducting gap induced by a competing odd-parity Fulde–Ferrel–Larkin–Ovchinnikov superconductivity in deeply underdoped cuprates. Preprint at http://arXiv.org/abs/1312.0544 (2013).

  142. Mistark, P., Markiewicz, S. R. & Bansil, A. Nanoscale phase separation in deep underdoped Bi2Sr2CuO6 + δ and Ca2CuO2Cl2. Preprint at http://arXiv.org/abs/1405.3992 (2014).

  143. Dipasupil, R. M. et al. Pseudogap in the tunneling spectra of slightly overdoped Bi2212. Physica C 364, 604–607 (2001).

    Article  ADS  Google Scholar 

  144. Ozyuzer, L., Zasadzinski, J. F., Gray, K. E., Kendziora, C. & Miyakawa, N. Absence of pseudogap in heavily overdoped Bi2Sr2CaCu2O8 + δ from tunneling spectroscopy of break junctions. Europhys. Lett. 58, 589–595 (2002).

    Article  ADS  Google Scholar 

  145. Venturini, F. et al. Observation of an unconventional metal–insulator transition in overdoped CuO2 compounds. Phys. Rev. Lett. 89, 107003 (2002).

    Article  ADS  Google Scholar 

  146. Gomes, K. K. et al. Visualizing pair formation on the atomic scale in the high-Tc superconductor Bi2Sr2CaCu2O8 + δ . Nature 447, 569–572 (2007).

    Article  ADS  Google Scholar 

  147. Gabovich, A. M. et al. Competition of superconductivity and charge density waves in cuprates: Recent evidence and interpretation. Adv. Condens. Matter. Phys. 2010, 681070 (2010).

    Article  Google Scholar 

  148. Moon, E. G. & Sachdev, S. Quantum critical point shifts under superconductivity: Pnictides and cuprates. Phys. Rev. B 82, 104516 (2010).

    Article  ADS  Google Scholar 

  149. Nandi, S. et al. Anomalous suppression of the orthorhombic lattice distortion in superconducting Ba(Fe1 − xCox)2As2 single crystals. Phys. Rev. Lett. 104, 057006 (2010).

    Article  ADS  Google Scholar 

  150. Wiesenmayer, E. et al. Microscopic coexistence of superconductivity and magnetism in Ba1 − xKxFe2As2 . Phys. Rev. Lett. 107, 237001 (2011).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  152. Dipasupil, R. M., Oda, M., Momono, N. & Ido, M. Energy gap evolution in the tunneling spectra of Bi2Sr2CaCu2O8 + δ . J. Phys. Soc. Jpn 71, 1535–1540 (2002).

    Article  ADS  Google Scholar 

  153. Valla, T., Fedorov, A. V., Lee, J., Davis, J. C. & Gu, G. D. The ground state of the pseudogap in cuprate superconductors. Science 314, 1914–1916 (2006).

    Article  ADS  Google Scholar 

  154. Chatterjee, U. et al. Observation of a d-wave nodal liquid in highly underdoped Bi2Sr2CaCu2O8 + δ . Nature Phys. 6, 99–103 (2010).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  156. Randeria, M. et al. Momentum distribution sum rule for angle-resolved photoemission. Phys. Rev. Lett. 74, 4951–4954 (1995).

    Article  ADS  Google Scholar 

  157. Vishik, I. M., Hashimoto, M., Lee, W. S., Devereaux, T. P. & Shen, Z. X. Ubiquitous antinodal quasiparticles and deviation from simple d-wave form in underdoped Bi-2212. Preprint at http://arXiv.org/abs/1405.4961 (2014).

  158. Norman, M. R., Kanigel, A., Randeria, M., Chatterjee, U. & Campuzano, J. C. Modeling the Fermi arc in underdoped cuprates. Phys. Rev. B 76, 174501 (2007).

    Article  ADS  Google Scholar 

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Acknowledgements

We acknowledge Y. L. Chen, K. Tanaka, W-S. Lee and B. Moritz for sharing their ARPES data and for making the figures, and A. Fujimori, Z. Hussain and D. H. Lu for long-term collaboration. This work is supported by the Department of Energy, Office of Basic Energy Science, Division of Materials Science.

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Author notes

  1. Inna M. Vishik

    Present address: Present address: Department Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.,

  2. Rui-Hua He

    Present address: Present address: Department of Physics, Boston College, Chestnut Hill, Massachusetts 02467, USA.,

Authors and Affiliations

  1. Stanford Synchrotron Radiation Lightsource, SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA

    Makoto Hashimoto

  2. Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA

    Inna M. Vishik, Rui-Hua He, Thomas P. Devereaux & Zhi-Xun Shen

  3. Geballe Laboratory for Advanced Materials, Stanford University, Stanford, California 94305, USA

    Inna M. Vishik, Rui-Hua He, Thomas P. Devereaux & Zhi-Xun Shen

  4. Departments of Physics and Applied Physics, Stanford University, Stanford, California 94305, USA

    Inna M. Vishik, Rui-Hua He & Zhi-Xun Shen

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Hashimoto, M., Vishik, I., He, RH. et al. Energy gaps in high-transition-temperature cuprate superconductors. Nature Phys 10, 483–495 (2014). https://doi.org/10.1038/nphys3009

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