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Spectroscopic Imaging STM: Atomic-Scale Visualization of Electronic Structure and Symmetry in Underdoped Cuprates

Chapter
Part of the Springer Series in Solid-State Sciences book series (SSSOL, volume 180)

Abstract

Atomically resolved spectroscopic imaging STM (SI-STM) has played a pivotal role in visualization of the electronic structure of cuprate high temperature superconductors. In both the d-wave superconducting (dSC) and the pseudogap (PG) phases of underdoped cuprates, two distinct types of electronic states are observed when using SI-STM. The first consists of the dispersive Bogoliubov quasiparticles of a homogeneous d-wave superconductor existing in an energy range \(\vert {}E\vert {} \le {}\varDelta _{0}\) and only upon an arc in momentum space (k-space) that terminates close to the lines connecting k \(=\) \(\pm {}(\pi {}/a_{0},0)\) to k \(=\) \(\pm {}(0, \pi {}/a_{0})\). This ‘nodal’ arc shrinks continuously as electron density increases towards half filling. In both phases, the only broken symmetries detected in the \(\vert E\vert \le \varDelta _{0}\) states are those of a d-wave superconductor. The second type of electronic state occurs near the pseudogap energy scale \(\vert E\vert \sim \varDelta _{1}\) or equivalently near the ‘antinodal’ regions k \(=\) \(\pm (\pi /a_{0},0)\) and k \(=\) \(\pm (0, \pi /a_{0})\). These states break the expected 90\(^{\circ }\)-rotational (C\(_{4}\)) symmetry of electronic structure within each CuO\(_{2}\) unit cell, at least down to 180\(^{\circ }\)-rotational (C\(_{2}\)), symmetry. This intra-unit-cell symmetry breaking is interleaved with the incommensurate conductance modulations locally breaking both rotational and translational symmetries. Their wavevector S is always found to be determined by the k-space points where Bogoliubov quasiparticle interference terminates along the line joining \(\mathbf k =(0,\pm \pi /a_{0})\) to \(\mathbf k =(\pm \pi /a_{0},0)\), and thus diminishes continuously with doping. The symmetry properties of these \(\vert E\vert \sim \varDelta _1\) states are indistinguishable in the dSC and PG phases. While the relationship between the \(\vert E\vert \sim \varDelta _1\) broken symmetry states and the \(\vert E\vert \le \varDelta _{0}\) Bogoliubov quasiparticles of the homogeneous superconductor is not yet fully understood, these two sets of phenomena are linked inextricably because the k-space locations where the latter disappears are always linked by the modulation wavevectors of the former.

Keywords

Incommensurate Modulation Underdoped Cuprates Bogoliubov Quasiparticle Break Symmetry State Octet Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgments

We acknowledge and thank all our collaborators: E.-A. Kim, M.J. Lawler, J.W. Alldredge, T. Hanaguri, P.J. Hirschfeld, J.E. Hoffman, E.W. Hudson, Y. Kohsaka, K.M. Lang, C. Lupien, Jhinhwan Lee, Jinho Lee, V. Madhavan, K. McElroy, J. Orenstein, S.H. Pan, R. Simmonds, A. Schmidt, J. Sethna, J. Slezak, H. Takagi, C. Taylor, P. Wahl and M. Wang. Preparation of this manuscript was supported by the Center for Emergent Superconductivity, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Basic Energy Sciences under Award Number DE-2009-BNL-PM015. We also acknowledge support during the writing of this article by US DOE under contract DEAC02-98CH10886, as well as by a Grant-in-Aid for Scientific Research from the Ministry of Science and Education (Japan) and the Global Centers of Excellence Program for Japan Society for the Promotion of Science. C.K.K. was supported under the FlucTeam program at Brookhaven National Laboratory under contract DE-AC02-98CH10886. M.H. acknowledges funding the Office of Naval Research under Award N00014-13-1-0047. S.M. acknowledges support from NSF Grant DMR-1120296 to the Cornell Center for Materials Research.

References

  1. 1.
    J. Zaanen, G.A. Sawatzky, J.W. Allen, Phys. Rev. Lett. 55, 418 (1985)Google Scholar
  2. 2.
    C. Weber, C. Yee, K. Haule, G. Kotliar, Euro. Phys. Lett. 100, 37001 (2012)ADSGoogle Scholar
  3. 3.
    P.W. Anderson, Phys. Rev. 79, 350 (1950)zbMATHADSGoogle Scholar
  4. 4.
    P.W. Anderson, Sci. 235, 1196 (1987)ADSGoogle Scholar
  5. 5.
    C.T. Chen, F. Sette, Y. Ma, M.S. Hybertsen, E.B. Stechel, W.M.C. Foulkes, M. Schulter, S.W. Cheong, A.S. Cooper, L.W. Rupp Jr, B. Batlogg, Y.L. Soo, Z.H. Ming, A. Krol, Y.H. Kao, Phys. Rev. Lett. 66, 104 (1991)ADSGoogle Scholar
  6. 6.
    Y. Sakurai, M. Itou, B. Barbiellini, P.E. Mijnarends, R.S. Markiewicz, S. Kaprzyk, J.M. Gillet, S. Wakimoto, M. Fujita, S. Basak, Y.J. Wang, W. Al-Sawai, H. Lin, A. Bansil, K. Yamada, Science 332, 698 (2011)ADSGoogle Scholar
  7. 7.
    Y. Kohsaka, T. Hanaguri, M. Azuma, M. Takano, J.C. Davis, H. Takagi, Nat. Phys. 8, 534 (2012)Google Scholar
  8. 8.
    J. Orenstein, A.J. Millis, Science 288, 468 (2000)ADSGoogle Scholar
  9. 9.
    T. Timusk, B. Statt, Rep. Prog. Phys. 62, 61 (1999)ADSGoogle Scholar
  10. 10.
    S. Hüefner, M.A. Hossain, A. Damascelli, G.A. Sawatzky, Rep. Prog. Phys. 71, 062501 (2008)ADSGoogle Scholar
  11. 11.
    A. Damascelli, Z. Hussain, Z.X. Shen, Rev. Mod. Phys. 75, 473 (2003)ADSGoogle Scholar
  12. 12.
    J.C. Campuzano, M.R. Norman, M. Randeria, The Physics of Superconductors (Springer, New York, 2004)Google Scholar
  13. 13.
    M.R. Norman, C. Pépin, Rep. Prog. Phys. 66, 1547 (2003)ADSGoogle Scholar
  14. 14.
    F.C. Zhang, C. Gros, T.M. Rice, H. Shiba, Super. Sci. Tech. 1, 36 (1988)ADSGoogle Scholar
  15. 15.
    G. Kotliar, Phys. Rev. B 37, 3664 (1988)ADSGoogle Scholar
  16. 16.
    A. Paramekanti, M. Randeria, N. Trivedi, Phys. Rev. Lett. 87, 217002 (2001)ADSGoogle Scholar
  17. 17.
    P.W. Anderson, P.A. Lee, M. Randeria, T.M. Rice, N. Trivedi, F.C. Zhang, J. Phys. Cond. Matt. 16, R755 (2004)ADSGoogle Scholar
  18. 18.
    K.Y. Yang, T.M. Rice, F.C. Zhang, Phys. Rev. B 73, 174501 (2006)ADSGoogle Scholar
  19. 19.
    M. Randeria, N. Trivedi, A. Moreo, R.T. Scalettar, Phys. Rev. Lett. 69, 2001 (1999)ADSGoogle Scholar
  20. 20.
    V.J. Emery, S.A. Kivelson, Nature 374, 434 (1995)ADSGoogle Scholar
  21. 21.
    M. Franz, A.J. Millis, Phys. Rev. B 58, 14572 (1998)ADSGoogle Scholar
  22. 22.
    E.W. Carlson, S.A. Kivelson, V.J. Emery, E. Manousakis, Phys. Rev. Lett. 83, 612 (1999)ADSGoogle Scholar
  23. 23.
    H.J. Kwon, A.T. Dorsey, P.J. Hirschfeld, Phys. Rev. Lett. 86, 3875 (2001)ADSGoogle Scholar
  24. 24.
    E. Berg, E. Altman, Phys. Rev. Lett. 99, 247001 (2007)ADSGoogle Scholar
  25. 25.
    C.M. Varma, Phys. Rev. B 73, 155113 (2006)ADSGoogle Scholar
  26. 26.
    P.A. Lee, N. Nagaosa, X.G. Wen, Rev. Mod. Phys. 78, 17 (2006)ADSGoogle Scholar
  27. 27.
    S. Chakravarty, R.B. Laughlin, D.K. Morr, C. Nayak, Phys. Rev. B 63, 094503 (2001)ADSGoogle Scholar
  28. 28.
    C. Honerkamp, H.C. Fu, D.H. Lee, Phys. Rev. B 75, 014503 (2007)ADSGoogle Scholar
  29. 29.
    D.M. Newns, C.C. Tsuei, Nat. Phys. 3, 184 (2007)Google Scholar
  30. 30.
    J. Zaanen, O. Gunnarsson, Phys. Rev. B 40, 7391 (1989)ADSGoogle Scholar
  31. 31.
    V.J. Emery, S.A. Kivelson, J.M. Tranquada, Proc. Natl. Acad. Sci. 96, 8814 (1999)ADSGoogle Scholar
  32. 32.
    S.R. White, D.J. Scalapino, Phys. Rev. Lett. 80, 1272 (1998)ADSGoogle Scholar
  33. 33.
    S.A. Kivelson, E. Fradkin, V.J. Emery, Nature 393, 550 (1998)ADSGoogle Scholar
  34. 34.
    M. Vojta, S. Sachdev, Phys. Rev. Lett. 83, 3916 (1999)ADSGoogle Scholar
  35. 35.
    S.A. Kivelson, I.P. Bindloss, E. Fradkin, V. Oganesyan, J.M. Tranquada, A. Kapitulnik, C. Howald, Rev. Mod. Phys. 75, 1201 (2003)ADSGoogle Scholar
  36. 36.
    S. Sachdev, Rev. Mod. Phys. 75, 913 (2003)ADSGoogle Scholar
  37. 37.
    M. Vojta, Adv. Phys. 58, 699 (2009)ADSGoogle Scholar
  38. 38.
    E.A. Kim, M.J. Lawler, P. Oreto, S. Sachdev, E. Fradkin, S.A. Kivelson, Phys. Rev. B 77, 184514 (2008)ADSGoogle Scholar
  39. 39.
    E. Fradkin, S.A. Kivelson, M.J. Lawler, J.P. Eisenstein, A.P. Mackenzie, Annu. Rev. Condens. Matter Phys. 1, 153 (2010)ADSGoogle Scholar
  40. 40.
    N. Gedik, J. Orenstein, R. Liang, D.A. Bonn, W.N. Hardy, Science 300, 1410 (2003)ADSGoogle Scholar
  41. 41.
    G. Deutscher, Nature 397, 410 (1999)ADSGoogle Scholar
  42. 42.
    M.L. Tacon, A. Sacuto, A. Georges, G. Kotliar, Y. Gallais, D. Colson, A. Forget, Nat. Phys. 2, 537 (2006)Google Scholar
  43. 43.
    R. Khasanov, T. Kondo, M. Bendele, Y. Hamaya, A. Kaminski, S.L. Lee, S.J. Ray, T. Takeuchi, Phys. Rev. B 82, 020511(R) (2010)ADSGoogle Scholar
  44. 44.
    M.R. Norman, H. Ding, M. Randeria, J.C. Campuzano, T. Yokoya, T. Takeuchi, T. Takahashi, T. Mochiku, K. Kadowaki, P. Guptasarma, D.G. Hinks, Nature 392, 157 (1998)ADSGoogle Scholar
  45. 45.
    K.M. Shen, F. Ronning, D.H. Lu, F. Baumberger, N.J.C. Ingle, W.S. Lee, W. Meevasana, Y. Kohsaka, M. Azuma, M. Takano, H. Takagi, Z.X. Shen, Science 307, 901 (2005)ADSGoogle Scholar
  46. 46.
    K. Tanaka, W.S. Lee, D.H. Lu, A. Fujimori, T. Fujii, Risdiana, I. Terasaki, D.J. Scalapino, T.P. Devereaux, Z. Hussain. Science 314, 1910 (2006)ADSGoogle Scholar
  47. 47.
    A. Kanigel, M.R. Norman, M. Randeria, U. Chatterjee, S. Souma, A. Kaminski, H.M. Fretwell, S. Rosenkranz, M. Shi, T. Sato, T. Takahashi, Z.Z. Li, H. Raffy, K. Kadowaki, D. Hinks, L. Ozyuzer, J.C. Campuzano, Nat. Phys. 2, 447 (2006)Google Scholar
  48. 48.
    A. Kanigel, U. Chatterjee, M. Randeria, M.R. Norman, S. Souma, M. Shi, Z.Z. Li, H. Raffy, J.C. Campuzano, Phys. Rev. Lett. 99, 157001 (2007)ADSGoogle Scholar
  49. 49.
    T. Kondo, R. Khasanov, T. Takeuchi, J. Schmalian, A. Kaminski, Nature 457, 296 (2009)ADSGoogle Scholar
  50. 50.
    H.B. Yang, J.D. Rameau, Z.H. Pan, G.D. Gu, P.D. Johnson, H. Claus, D.G. Hinks, T.E. Kidd, Phys. Rev. Lett. 107, 047003 (2011)ADSGoogle Scholar
  51. 51.
    Ch. Renner, B. Revaz, J.Y. Genoud, K. Kadowaki, Ø. Fischer, Phys. Rev. Lett. 80, 149 (1998)ADSGoogle Scholar
  52. 52.
    Ø. Fischer, M. Kugler, I. Maggio-Aprile, C. Berthod, Ch. Renner, Rev. Mod. Phys. 79, 353 (2007)ADSGoogle Scholar
  53. 53.
    K. McElroy, D.H. Lee, J.E. Hoffman, K.M. Lang, J. Lee, E.W. Hudson, H. Eisaki, S. Uchida, J.C. Davis, Phys. Rev. Lett. 94, 197005 (2005)ADSGoogle Scholar
  54. 54.
    K. McElroy, J. Lee, J.A. Slezak, D.H. Lee, H. Eisaki, S. Uchida, J.C. Davis, Sci. 309, 1048 (2005)ADSGoogle Scholar
  55. 55.
    J.W. Alldredge, J. Lee, K. McElroy, M. Wang, K. Fujita, Y. Kohsaka, C. Taylor, H. Eisaki, S. Uchida, P.J. Hirschfeld, J.C. Davis, Nat. Phys. 4, 319 (2008)Google Scholar
  56. 56.
    J.E. Hoffman, K. McElroy, D.H. Lee, K.M. Lang, H. Eisaki, S. Uchida, J.C. Davis, Sci. 297, 1148 (2002)ADSGoogle Scholar
  57. 57.
    K. McElroy, R.W. Simmonds, J.E. Hoffman, D.H. Lee, J. Orenstein, H. Eisaki, S. Uchida, J.C. Davis, Nature 422, 592 (2003)ADSGoogle Scholar
  58. 58.
    T. Hanaguri, Y. Kohsaka, J.C. Davis, C. Lupien, I. Yamada, M. Azuma, M. Takano, K. Ohishi, M. Ono, H. Takagi, Nat. Phys. 3, 865 (2007)Google Scholar
  59. 59.
    W.D. Wise, K. Chatterjee, M.C. Boyer, T. Kondo, T. Takeuchi, H. Ikuta, Z. Xu, J. Wen, G.D. Gu, Y. Wang, E.W. Hudson, Nat. Phys. 5, 213 (2009)Google Scholar
  60. 60.
    Y. Kohsaka, C. Taylor, K. Fujita, A. Schmidt, C. Lupien, T. Hanaguri, M. Azuma, M. Takano, H. Eisaki, H. Takagi, S. Uchida, J.C. Davis, Science 315, 1380 (2007)ADSGoogle Scholar
  61. 61.
    Y. Kohsaka, C. Taylor, P. Wahl, A. Schmidt, J. Lee, K. Fujita, J.W. Alldredge, K. McElroy, J. Lee, H. Eisaki, S. Uchida, D.H. Lee, J.C. Davis, Nature 454, 1072 (2008)ADSGoogle Scholar
  62. 62.
    J. Lee, K. Fujita, A.R. Schmidt, C.K. Kim, H. Eisaki, S. Uchida, J.C. Davis, Science 325, 1099 (2009)ADSGoogle Scholar
  63. 63.
    S.H. Pan, J.P. O’neal, R.L. Badzey, C. Chamon, H. Ding, J.R. Engelbrecht, Z. Wang, H. Eisaki, S. Uchida, A.K. Gupta, K.W. Ng, E.W. Hudson, K.M. Lang, J.C. Davis, Nature 413, 282 (2001)ADSGoogle Scholar
  64. 64.
    K.M. Lang, V. Madhavan, J.E. Hoffman, E.W. Hudson, H. Eisaki, S. Uchida, J.C. Davis, Nature 415, 412 (2002)ADSGoogle Scholar
  65. 65.
    T. Cren, D. Roditchev, W. Sacks, J. Klein, Euro. Phys. Lett. 54, 84 (2001)ADSGoogle Scholar
  66. 66.
    C. Howald, P. Fournier, A. Kapitulnik, Phys. Rev. B 64, 100504 (2001)ADSGoogle Scholar
  67. 67.
    A. Matsuda, T. Fujii, T. Watanabe, Phys. C 388, 207 (2003)ADSGoogle Scholar
  68. 68.
    M.C. Boyer, W.D. Wise, K. Chatterjee, M. Yi, T. Kondo, T. Takeuchi, H. Ikuta, E.W. Hudson, Nat. Phys. 3, 802 (2007)Google Scholar
  69. 69.
    K.K. Gomes, A.N. Pasupathy, A. Pushp, S. Ono, Y. Ando, A. Yazdani, Nature 447, 569 (2007)ADSGoogle Scholar
  70. 70.
    A. Pushp, C.V. Parker, A.N. Pasupathy, K.K. Gomes, S. Ono, J.S. Wen, Z. Xu, G.D. Gu, A. Yazdani, Science 324, 1689 (2009)ADSGoogle Scholar
  71. 71.
    M.J. Lawler, K. Fujita, J. Lee, A.R. Schmidt, Y. Kohsaka, C.K. Kim, H. Eisaki, S. Uchida, J.C. Davis, J.P. Sethna, E.A. Kim, Nature 466, 347 (2010)ADSGoogle Scholar
  72. 72.
    A. Mesaros, K. Fujita, H. Eisaki, S. Uchida, J.C. Davis, S. Sachdev, J. Zaanen, M.J. Lawler, E.A. Kim, Science 333, 426 (2011)ADSGoogle Scholar
  73. 73.
    E.H.S. Neto, P. Aynajian, R.E. Baumbach, E.D. Bauer, J. Mydosh, S. Ono, A. Yazdani, Phys. Rev. B 87, 161117(R) (2013)ADSGoogle Scholar
  74. 74.
    S.H. Pan, E.W. Hudson, J.C. Davis, Rev. Sci. Instrum. 70, 1459 (1999)ADSGoogle Scholar
  75. 75.
    H. Hobou, S. Ishida, K. Fujita, M. Ishikado, K.M. Kojima, H. Eisaki, S. Uchida, Phys. Rev. B 79, 064507 (2009)ADSGoogle Scholar
  76. 76.
    J.A. Slezak, J. Lee, M. Wang, K. McElroy, K. Fujita, B.M. Andersen, P.J. Hirschfeld, H. Eisaki, S. Uchida, J.C. Davis, Proc. Natl. Acad. Sci. 105, 3203 (2008)ADSGoogle Scholar
  77. 77.
    P.M. Chaikin, T.C. Lubensky, Principles of condensed matter physics (Cambridge University Press, Cambridge, 2010)Google Scholar
  78. 78.
    A.V. Balatsky, I. Vekhter, J.X. Zhu, Rev. Mod. Phys. 78, 373 (2006)ADSGoogle Scholar
  79. 79.
    A.A. Abrikosov, L.P. Gor’kov, Sov. Phys. JETP 12, 1243 (1961)Google Scholar
  80. 80.
    Y. Fukuzumi, K. Mizuhashi, K. Takenaka, S. Uchida, Phys. Rev. Lett. 76, 684 (1996)ADSGoogle Scholar
  81. 81.
    A.P. Mackenzie, R.K.W. Haselwimmer, A.W. Tyler, G.G. Lonzarich, Y. Mori, S. Nishizaki, Y. Maeno, Phys. Rev. Lett. 80, 161 (1998)ADSGoogle Scholar
  82. 82.
    H. Shiba, Prog. Theor. Phys. 40, 435 (1968)ADSGoogle Scholar
  83. 83.
    S.H. Pan, E.W. Hudson, K.M. Lang, H. Eisaki, S. Uchida, J.C. Davis, Nature 403, 746 (2000)ADSGoogle Scholar
  84. 84.
    M.H. Hamidian, I.A. Firmo, K. Fujita, S. Mukhopadhyay, J.W. Orenstein, H. Eisaki, S. Uchida, M.J. Lawler, E.A. Kim, J.C. Davis, New J. Phys. 14, 053017 (2012)ADSGoogle Scholar
  85. 85.
    E.W. Hudson, K.M. Lang, V. Madhavan, S.H. Pan, H. Eisaki, S. Uchida, J.C. Davis, Nature 411, 920 (2001)ADSGoogle Scholar
  86. 86.
    T. Machida, T. Kato, H. Nakamura, M. Fujimoto, T. Mochiku, S. Ooi, A.D. Thakur, H. Sakata, K. Hirata, Phys. Rev. B 82, 180507(R) (2010)ADSGoogle Scholar
  87. 87.
    J. E. Hoffman, A search for alternative electronic order in the high temperature superconductor Bi\(_2\)Sr\(_2\)CaCu\(_2\)O\(_{8+\delta }\) by scanning tunneling microscopy. Ph.D. thesis, University of California, Berkeley (2003).Google Scholar
  88. 88.
    N. Jenkins, Y. Fasano, C. Berthod, I. Maggio-Aprile, A. Piriou, E. Giannini, B.W. Hoogenboom, C. Hess, T. Cren, Ø. Fischer, Phys. Rev. Lett. 103, 227001 (2009)ADSGoogle Scholar
  89. 89.
    S. Maekawa, Physics of Transition Metal Oxides (Springer, Berlin, 2004)Google Scholar
  90. 90.
    H. Eisaki, N. Kaneko, D.L. Feng, A. Damascelli, P.K. Mang, K.M. Shen, Z.X. Shen, M. Greven, Phys. Rev. B 69, 064512 (2004)ADSGoogle Scholar
  91. 91.
    Q.H. Wang, J.H. Han, D.H. Lee, Phys. Rev. B 65, 054501 (2001)ADSGoogle Scholar
  92. 92.
    I. Martin, A.V. Balatsky, Phys. C 357, 46 (2001)ADSGoogle Scholar
  93. 93.
    J.X. Zhu, K.H. Ahn, Z. Nussinov, T. Lookman, A.V. Balatsky, A.R. Bishop, Phys. Rev. Lett. 91, 057004 (2003)ADSGoogle Scholar
  94. 94.
    E. Kaneshita, I. Martin, A.R. Bishop, J. Phys. Soc. Jpn. 73, 3223 (2004)zbMATHADSGoogle Scholar
  95. 95.
    T.S. Nunner, B.M. Andersen, A. Melikyan, P.J. Hirschfeld, Phys. Rev. Lett. 95, 177003 (2005)ADSGoogle Scholar
  96. 96.
    Y. He, T.S. Nunner, P.J. Hirschfeld, H.P. Cheng, Phys. Rev. Lett. 96, 197002 (2006)ADSGoogle Scholar
  97. 97.
    M. Mori, G. Khaliullin, T. Tohyama, S. Maekawa, Phys. Rev. Lett. 101, 247003 (2008)ADSGoogle Scholar
  98. 98.
    K. Fujita, T. Noda, K.M. Kojima, H. Eisaki, S. Uchida, Phys. Rev. Lett. 95, 097006 (2005)ADSGoogle Scholar
  99. 99.
    I. Zeljkovic, Z. Xu, J. Wen, G. Gu, R.S. Markiewicz, J.E. Hoffman, Science 337, 320 (2012)ADSGoogle Scholar
  100. 100.
    Q.H. Wang, D.H. Lee, Phys. Rev. B 67, 020511 (2003)ADSGoogle Scholar
  101. 101.
    L. Capriotti, D.J. Scalapino, R.D. Sedgewick, Phys. Rev. B 68, 014508 (2003)ADSGoogle Scholar
  102. 102.
    T.S. Nunner, W. Chen, B.M. Andersen, A. Melikyan, P.J. Hirschfeld, Phys. Rev. B 73, 104511 (2006)ADSGoogle Scholar
  103. 103.
    J. Mesot, M.R. Norman, H. Ding, M. Randeria, J.C. Campuzano, A. Paramekanti, H.M. Fretwell, A. Kaminski, T. Takeuchi, T. Yokoya, T. Sato, T. Takahashi, T. Mochiku, K. Kadowaki, Phys. Rev. Lett. 83, 840 (1999)ADSGoogle Scholar
  104. 104.
    M.P. Allan, A.W. Rost, A.P. Mackenzie, Y. Xie, J.C. Davis, K. Kihou, C.H. Lee, A. Iyo, H. Eisaki, T.M. Chuang, Science 336, 563 (2012)ADSGoogle Scholar
  105. 105.
    B.M. Andersen, P.J. Hirschfeld, Phys. Rev. B 79, 144515 (2009)ADSGoogle Scholar
  106. 106.
    T. Pereg-Barnea, M. Franz, Phys. Rev. B 68, 180506 (2003)ADSGoogle Scholar
  107. 107.
    S. Misra, M. Vershinin, P. Phillips, A. Yazdani, Phys. Rev. B 70, 220503 (2004)ADSGoogle Scholar
  108. 108.
    D. Wulin, Y. He, C.C. Chien, D.K. Morr, K. Levin, Phys. Rev. B 80, 134504 (2009)ADSGoogle Scholar
  109. 109.
    J. Corson, R. Mallozzi, J. Orenstein, J.N. Eckstein, I. Bozovic, Nature 398, 221 (1999)ADSGoogle Scholar
  110. 110.
    Z.A. Xu, N.P. Ong, Y. Wang, T. Kakeshita, S. Uchida, Nature 406, 486 (2000)ADSGoogle Scholar
  111. 111.
    Y. Wang, L. Li, N.P. Ong, Phys. Rev. B 73, 024510 (2006)ADSGoogle Scholar
  112. 112.
    Y. Wang, L. Li, M.J. Naughton, G.D. Gu, S. Uchida, N.P. Ong, Phys. Rev. Lett. 95, 247002 (2005)ADSGoogle Scholar
  113. 113.
    L. Li, Y. Wang, M.J. Naughton, S. Ono, Y. Ando, N.P. Ong, Europhys. Lett. 72, 451 (2005)ADSGoogle Scholar
  114. 114.
    N. Bergeal, J. Lesueur, M. Aprili, G. Faini, J.P. Contour, B. Lerido, Nat. Phys. 4, 608 (2008)Google Scholar
  115. 115.
    Y. Chen, T.M. Rice, F.C. Zhang, Phys. Rev. Lett. 97, 237004 (2006)ADSGoogle Scholar
  116. 116.
    J.M. Tranquada, B.J. Sternlieb, J.D. Axe, Y. Nakamura, S. Uchida, Nature 375, 561 (1995)ADSGoogle Scholar
  117. 117.
    J.M. Tranquada, H. Woo, T.G. Perring, H. Goka, G.D. Gu, G. Xu, M. Fujita, K. Yamada, Nature 429, 534 (2004)ADSGoogle Scholar
  118. 118.
    P. Abbamonte, A. Rusydi, S. Smadici, G.D. Gu, G.A. Sawatzky, D.L. Feng, Nat. Phys. 1, 155 (2005)Google Scholar
  119. 119.
    Y.J. Kim, G.D. Gu, T. Gog, D. Casa, Phys. Rev. B 77, 064520 (2008)ADSGoogle Scholar
  120. 120.
    K. Fujita, M.H. Hamidian, S.D. Edkins, C. Kim, Y. Kohsaka, M. Azuma, M. Takano, H. Takagi, H. Eisaki, S. Uchida, A. Allais, M.J. Lawler, E.A. Kim, S. Sachdev, J.C. Davis, Proc. Nat’l. Acad. Sci. 111, E3026 (2014)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.LASSP, Department of PhysicsCornell UniversityIthacaUSA
  2. 2.CMPMS DepartmentBrookhaven National LaboratoryUptonUSA
  3. 3.Kavli Institute at Cornell for NanoscienceCornell UniversityIthacaUSA
  4. 4.National Institute of Advanced Industrial Science and Technology (AIST)TsukubaJapan
  5. 5.Department of PhysicsUniversity of TokyoBunkyo-kuJapan
  6. 6.School of Physics and AstronomyUniversity of St. AndrewsScotlandUK

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