Phase diagram of underdoped cuprate superconductors: Effects of Cooper-pair phase fluctuations

Physical Review B - Condensed Matter and Materials Physics

Volumn 66, Issue 9, 2002, Pages 945151-9451511

  Timm, C ^a   Manske, D ^a   Bennemann, K H ^a  

^a FREIE UNIVERSITÄT BERLIN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

COPPER COMPLEX;

ARTICLE; ELECTRIC CONDUCTIVITY; ELECTROMAGNETIC FIELD; GLASS TRANSITION TEMPERATURE; HYDRODYNAMICS; LINEAR SYSTEM; MATHEMATICAL ANALYSIS; MATHEMATICAL MODEL; MOLECULAR DYNAMICS; MOLECULAR INTERACTION; PHASE TRANSITION; SPIN LABELING; TEMPERATURE DEPENDENCE; VORTEX MOTION;

EID: 0036752396     PISSN: 01631829     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevB.66.094515     Document Type: Article

References (116)

1. Y.J. Uemura, G.M. Luke, B.J. Sternlieb, J.H. Brewer, J.F. Carolan, W.N. Hardy, R. Kadono, J.R. Kempton, R.F. Kiefl, S.R. Kreitzman, P. Mulhern, T.M. Riseman, D.Ll. Williams, B.X. Yang, S. Uchida, H. Takagi, J. Gopalakrishnan, A.W. Sleight, M.A. Subramanian, C.L. Chien, M.Z. Cieplak, G. Xiao, V.Y. Lee, B.W. Statt, C.E. Stronach, W.J. Kossler, and X.H. Yu, Phys. Rev. Lett. 62, 2317 (1989).
2. C.C. Tsuei, J.R. Kirtley, C.C. Chi, L.S. Yu-Jahnes, A. Gupta, T. Shaw, J.Z. Sun, and M.B. Ketchen, Phys. Rev. Lett. 73, 593 (1994); J.R. Kirtley, C.C. Tsuei, M. Rupp, J.Z. Sun, L.S. Yu-Jahnes, A. Gupta, M.B. Ketchen, K.A. Moler, and M. Bhushan, ibid. 76, 1336 (1996).
3. C.C. Tsuei, J.R. Kirtley, C.C. Chi, L.S. Yu-Jahnes, A. Gupta, T. Shaw, J.Z. Sun, and M.B. Ketchen, Phys. Rev. Lett. 73, 593 (1994); J.R. Kirtley, C.C. Tsuei, M. Rupp, J.Z. Sun, L.S. Yu-Jahnes, A. Gupta, M.B. Ketchen, K.A. Moler, and M. Bhushan, ibid. 76, 1336 (1996).
4. J.M. Tranquada, B.J. Sternlieb, J.D. Axe, Y. Nakamura, and S. Uchida, Nature (London) 375, 561 (1995); P. Dai, H.A. Mook, and F. Dogan, Phys. Rev. Lett. 80, 1738 (1998); Z.-X. Shen, P.J. White, D.L. Feng, C. Kim, G.D. Gu, H. Ikeda, R. Yoshizaki, and N. Koshizuka, Science 280, 259 (1998).
5. J.M. Tranquada, B.J. Sternlieb, J.D. Axe, Y. Nakamura, and S. Uchida, Nature (London) 375, 561 (1995); P. Dai, H.A. Mook, and F. Dogan, Phys. Rev. Lett. 80, 1738 (1998); Z.-X. Shen, P.J. White, D.L. Feng, C. Kim, G.D. Gu, H. Ikeda, R. Yoshizaki, and N. Koshizuka, Science 280, 259 (1998).
6. J.M. Tranquada, B.J. Sternlieb, J.D. Axe, Y. Nakamura, and S. Uchida, Nature (London) 375, 561 (1995); P. Dai, H.A. Mook, and F. Dogan, Phys. Rev. Lett. 80, 1738 (1998); Z.-X. Shen, P.J. White, D.L. Feng, C. Kim, G.D. Gu, H. Ikeda, R. Yoshizaki, and N. Koshizuka, Science 280, 259 (1998).
7. S. Doniach and M. Inui, Phys. Rev. B 41, 6668 (1990).
8. B.K. Chakraverty, A. Taraphder, and M. Avignon, Physica C 235-240, 2323 (1994).
9. V.J. Emery and S.A. Kivelson, Nature (London) 374, 434 (1995).
10. J.R. Schrieffer, Theory of Superconductivity (Benjamin, New York, 1964).
11. F. Schäfer, C. Timm, D. Manske, and K.H. Bennemann, J. Low Temp. Phys. 117, 223 (1999); F. Schäfer (unpublished).
12. F. Schäfer, C. Timm, D. Manske, and K.H. Bennemann, J. Low Temp. Phys. 117, 223 (1999); F. Schäfer (unpublished).
13. J. Schmalian, S. Grabowski, and K.H. Bennemann, Phys. Rev. B 56, R509 (1997).
14. C. Meingast, V. Pasler, P. Nagel, A. Rykov, S. Tajima, and P. Olsson, Phys. Rev. Lett. 86, 1606 (2001).
15. E. Roddick and D. Stroud, Phys. Rev. Lett. 74, 1430 (1995).
16. E.W. Carlson, S.A. Kivelson, V.J. Emery, and E. Manousakis, Phys. Rev. Lett. 83, 612 (1999).
17. P.W. Anderson, Phys. Rev. 112, 1900 (1958).
18. A. Paramekanti, M. Randeria, T.V. Ramakrishnan, and S.S. Mandal, Phys. Rev. B 62, 6786 (2000).
19. H.-J. Kwon, A.T. Dorsey, and P.J. Hirschfeld, Phys. Rev. Lett. 86, 3875 (2001).
20. S.N. Artemenko and S.V. Remizov, Phys. Rev. Lett. 86, 708 (2001).
21. W.W. Warren, Jr., R.E. Walstedt, G.F. Brennert, R.J. Cava, R. Tycko, R.F. Bell, and G. Dabbagh, Phys. Rev. Lett. 62, 1193 (1989).
22. H.J. Tao, F. Lu, and E.J. Wolf, Physica C 282-287, 1507 (1997); C. Renner, B. Revaz, J.-Y. Genoud, K. Kadowaki, and Ø. Fischer, Phys. Rev. Lett. 80, 149 (1998).
23. H.J. Tao, F. Lu, and E.J. Wolf, Physica C 282-287, 1507 (1997); C. Renner, B. Revaz, J.-Y. Genoud, K. Kadowaki, and Ø. Fischer, Phys. Rev. Lett. 80, 149 (1998).
24. H. Takagi, B. Batlogg, H.L. Kao, J. Kwo, R.J. Cava, J.J. Krajewski, and W.F. Peck, Jr., Phys. Rev. Lett. 69, 2975 (1992).
25. D.N. Basov and T. Timusk, in Handbook on the Physics and Chemistry of Rare Earths, edited by K.A. Dschneidner, L. Eyring, and M.B. Maple (North-Holland, Amsterdam, 1999), and references therein.
26. T. Timusk and B.W. Statt, Rep. Prog. Phys. 62, 61 (1999), and references therein.
27. B. Giovannini and C. Berthod, Phys. Rev. B 63, 144516 (2001).
28. J.P. Rodriguez, Phys. Rev. B 49, 9831 (1994); J.P. Rodriguez and P. Lederer, ibid. 53, R11980 (1996).
29. J.P. Rodriguez, Phys. Rev. B 49, 9831 (1994); J.P. Rodriguez and P. Lederer, ibid. 53, R11980 (1996).
30. V.B. Geshkenbein, L.B. Ioffe, and A.I. Larkin, Phys. Rev. B 55, 3173 (1997).
31. A. Perali, C. Castellani, C. Di Castro, M. Grilli, E. Piegari, and A.A. Varlamov, Phys. Rev. B 62, R9295 (2000).
32. B. Batlogg and V.J. Emery, Nature (London) 382, 20 (1996); V.J. Emery, S.A. Kivelson, and O. Zachar, Phys. Rev. B 56, 6120 (1997).
33. B. Batlogg and V.J. Emery, Nature (London) 382, 20 (1996); V.J. Emery, S.A. Kivelson, and O. Zachar, Phys. Rev. B 56, 6120 (1997).
34. T. Dahm, D. Manske, and L. Tewordt, Phys. Rev. B 56, R11 419 (1997), and references therein.
35. R.S. Markiewicz, cond-mat/0108075 (unpublished).
36. D. Matthey, S. Gariglio, B. Giovannini, and J.-M. Triscone, Phys. Rev. B 64, 024513 (2001).
37. M.V. Feigel'man, Zh. Éksp. Teor. Fiz. 76 784 [Sov. Phys. JETP 49, 395 (1979)].
38. G. Blatter, M.V. Feigel'man, V.B. Geshkenbein, A.I. Larkin, and V.M. Vinokur, Rev. Mod. Phys. 66, 1125 (1994).
39. V.L. Berezinskii, Zh. Éksp. Teor. Fiz. 61 1144 (1971) [Sov. Phys. JETP 34, 610 (1972)]; J.M. Kosterlitz and D.J. Thouless, J. Phys. C 6, 1181 (1973); J.M. Kosterlitz, ibid., 7, 1046 (1974).
40. V.L. Berezinskii, Zh. Éksp. Teor. Fiz. 61 1144 (1971) [Sov. Phys. JETP 34, 610 (1972)]; J.M. Kosterlitz and D.J. Thouless, J. Phys. C 6, 1181 (1973); J.M. Kosterlitz, ibid., 7, 1046 (1974).
41. V.L. Berezinskii, Zh. Éksp. Teor. Fiz. 61 1144 (1971) [Sov. Phys. JETP 34, 610 (1972)]; J.M. Kosterlitz and D.J. Thouless, J. Phys. C 6, 1181 (1973); J.M. Kosterlitz, ibid., 7, 1046 (1974).
42. M.R. Beasley, J.E. Mooij, and T.P. Orlando, Phys. Rev. Lett. 42, 1165 (1979); S. Doniach and B.A. Huberman, ibid. 42, 1169 (1979); B.I. Halperin and D.R. Nelson, J. Low Temp. Phys. 36, 599 (1979); L.A. Turkevich, J. Phys. C 12, L385 (1979).
43. M.R. Beasley, J.E. Mooij, and T.P. Orlando, Phys. Rev. Lett. 42, 1165 (1979); S. Doniach and B.A. Huberman, ibid. 42, 1169 (1979); B.I. Halperin and D.R. Nelson, J. Low Temp. Phys. 36, 599 (1979); L.A. Turkevich, J. Phys. C 12, L385 (1979).
44. M.R. Beasley, J.E. Mooij, and T.P. Orlando, Phys. Rev. Lett. 42, 1165 (1979); S. Doniach and B.A. Huberman, ibid. 42, 1169 (1979); B.I. Halperin and D.R. Nelson, J. Low Temp. Phys. 36, 599 (1979); L.A. Turkevich, J. Phys. C 12, L385 (1979).
45. M.R. Beasley, J.E. Mooij, and T.P. Orlando, Phys. Rev. Lett. 42, 1165 (1979); S. Doniach and B.A. Huberman, ibid. 42, 1169 (1979); B.I. Halperin and D.R. Nelson, J. Low Temp. Phys. 36, 599 (1979); L.A. Turkevich, J. Phys. C 12, L385 (1979).
46. P. Minnhagen, Rev. Mod. Phys. 59, 1001 (1987).
47. A. Kovner and B. Rosenstein, Phys. Rev. B 42, 4748 (1990).
48. A. Buzdin and D. Feinberg, J. Phys. (Paris) 51, 1971 (1990); J.R. Clem, Phys. Rev. B 43, 7837 (1991).
49. A. Buzdin and D. Feinberg, J. Phys. (Paris) 51, 1971 (1990); J.R. Clem, Phys. Rev. B 43, 7837 (1991).
50. S.W. Pierson, Phys. Rev. Lett. 73, 2496 (1994); 75, 4674 (1995); Phys. Rev. B 51, 6663 (1995).
51. S.W. Pierson, Phys. Rev. Lett. 73, 2496 (1994); 75, 4674 (1995); Phys. Rev. B 51, 6663 (1995).
52. S.W. Pierson, Phys. Rev. Lett. 73, 2496 (1994); 75, 4674 (1995); Phys. Rev. B 51, 6663 (1995).
53. M. Friesen, Phys. Rev. B 51, 632 (1995).
54. C. Timm, Phys. Rev. B 52, 9751 (1995).
55. C. Timm, Phys. Rev. B 55, 3241 (1997).
56. S.W. Pierson, M. Friesen, S.M. Ammirata, J.C. Hunnicutt, and L.A. Gorham, Phys. Rev. B 60, 1309 (1999); S.W. Pierson and O.T. Valls, ibid. 61, 663 (2000).
57. S.W. Pierson, M. Friesen, S.M. Ammirata, J.C. Hunnicutt, and L.A. Gorham, Phys. Rev. B 60, 1309 (1999); S.W. Pierson and O.T. Valls, ibid. 61, 663 (2000).
58. D. Fay, J. Appel, C. Timm, and A. Zabel, Phys. Rev. B 63, 064509 (2001).
59. J.H. Schön, M. Dorget, F.C. Beuran, X.Z. Zu, E. Arushanov, C. Deville Cavellin, and M. Laguës, Nature (London) 414, 434 (2001).
60. P.C.E. Stamp, L. Forro, and C. Ayache, Phys. Rev. B 38, 2847 (1988).
61. S.N. Artemenko, I.G. Gorlova, and Y.I. Latyshev, Phys. Lett. A 138, 428 (1989).
62. S. Martin, A.T. Fiory, R.M. Fleming, G.P. Espinosa, and A.S. Cooper, Phys. Rev. Lett. 62, 677 (1989).
63. N.C. Yeh and C.C. Tsuei, Phys. Rev. B 39, 9708 (1989).
64. T. Freltoft, H.J. Jensen, and P. Minnhagen, Solid State Commun. 78, 635 (1991).
65. A.K. Pradhan, S.J. Hazell, J.W. Hodby, C. Chen, Y. Hu, and B.M. Wanklyn, Phys. Rev. B 47, 11 374 (1993).
66. J. Corson, R. Mallozzi, J. Orenstein, J.N. Eckstein, and I. Bozovic, Nature (London) 398, 221 (1999).
67. V. Ambegaokar, B.I. Halperin, D.R. Nelson, and E.D. Siggia, Phys. Rev. Lett. 40, 783 (1978); V. Ambegaokar and S. Teitel, Phys. Rev. B 19, 1667 (1979); V. Ambegaokar, B.I. Halperin, D.R. Nelson, and E.D. Siggia, ibid. 21, 1806 (1980).
68. V. Ambegaokar, B.I. Halperin, D.R. Nelson, and E.D. Siggia, Phys. Rev. Lett. 40, 783 (1978); V. Ambegaokar and S. Teitel, Phys. Rev. B 19, 1667 (1979); V. Ambegaokar, B.I. Halperin, D.R. Nelson, and E.D. Siggia, ibid. 21, 1806 (1980).
69. V. Ambegaokar, B.I. Halperin, D.R. Nelson, and E.D. Siggia, Phys. Rev. Lett. 40, 783 (1978); V. Ambegaokar and S. Teitel, Phys. Rev. B 19, 1667 (1979); V. Ambegaokar, B.I. Halperin, D.R. Nelson, and E.D. Siggia, ibid. 21, 1806 (1980).
70. Z.A. Xu, N.P. Ong, Y. Wang, T. Kakeshita, and S. Uchida, Nature (London) 406, 486 (2000); see also P.A. Lee, ibid., 406, 467 (2000).
71. Z.A. Xu, N.P. Ong, Y. Wang, T. Kakeshita, and S. Uchida, Nature (London) 406, 486 (2000); see also P.A. Lee, ibid., 406, 467 (2000).
72. Y. Wang, Z.A. Xu, T. Kakeshita, S. Uchida, S. Ono, Y. Ando, and N.P. Ong, Phys. Rev. B 64, 224519 (2001).
73. N.E. Bickers, D.J. Scalapino, and S.R. White, Phys. Rev. Lett. 62, 961 (1989); N.E. Bickers and D.J. Scalapino, Ann. Phys. (N.Y.) 193, 206 (1989).
74. N.E. Bickers, D.J. Scalapino, and S.R. White, Phys. Rev. Lett. 62, 961 (1989); N.E. Bickers and D.J. Scalapino, Ann. Phys. (N.Y.) 193, 206 (1989).
75. C.-H. Pao and N.E. Bickers, Phys. Rev. Lett. 72, 1870 (1994); Phys. Rev. B 51, 16 310 (1995).
76. C.-H. Pao and N.E. Bickers, Phys. Rev. Lett. 72, 1870 (1994); Phys. Rev. B 51, 16 310 (1995).
77. P. Monthoux and D.J. Scalapino, Phys. Rev. Lett. 72, 1874 (1994).
78. T. Dahm and L. Tewordt, Phys. Rev. Lett. 74, 793 (1995).
79. M. Langer, J. Schmalian, S. Grabowski, and K.H. Bennemann, Phys. Rev. Lett. 75, 4508 (1995); S. Grabowski, M. Langer, J. Schmalian, and K.H. Bennemann, Europhys. Lett. 34, 219 (1996); J. Schmalian, M. Langer, S. Grabowski, and K.H. Bennemann, Comput. Phys. Commun. 93, 141 (1996).
80. M. Langer, J. Schmalian, S. Grabowski, and K.H. Bennemann, Phys. Rev. Lett. 75, 4508 (1995); S. Grabowski, M. Langer, J. Schmalian, and K.H. Bennemann, Europhys. Lett. 34, 219 (1996); J. Schmalian, M. Langer, S. Grabowski, and K.H. Bennemann, Comput. Phys. Commun. 93, 141 (1996).
81. M. Langer, J. Schmalian, S. Grabowski, and K.H. Bennemann, Phys. Rev. Lett. 75, 4508 (1995); S. Grabowski, M. Langer, J. Schmalian, and K.H. Bennemann, Europhys. Lett. 34, 219 (1996); J. Schmalian, M. Langer, S. Grabowski, and K.H. Bennemann, Comput. Phys. Commun. 93, 141 (1996).
82. P.W. Anderson, Science 235, 1196 (1987); G. Baskaran, Z. Zou, and P.W. Anderson, Solid State Commun. 63, 973 (1987); P.W. Anderson, cond-mat/0201429 (unpublished).
83. P.W. Anderson, Science 235, 1196 (1987); G. Baskaran, Z. Zou, and P.W. Anderson, Solid State Commun. 63, 973 (1987); P.W. Anderson, cond-mat/0201429 (unpublished).
84. P.W. Anderson, Science 235, 1196 (1987); G. Baskaran, Z. Zou, and P.W. Anderson, Solid State Commun. 63, 973 (1987); P.W. Anderson, cond-mat/0201429 (unpublished).
85. G. Baym and L.P. Kadanoff, Phys. Rev. 124, 287 (1961); G. Baym, ibid. 127, 1391 (1962).
86. G. Baym and L.P. Kadanoff, Phys. Rev. 124, 287 (1961); G. Baym, ibid. 127, 1391 (1962).
87. L. Tewordt, J. Low Temp. Phys. 15, 349 (1974).
88. N.F. Berk and J.R. Schrieffer, Phys. Rev. Lett. 17, 433 (1966).
89. Y. Nambu, Phys. Rev. 117, 648 (1960).
90. H.-J. Kwon and A.T. Dorsey, Phys. Rev. B 59, 6438 (1999).
91. S.G. Sharapov, H. Beck, and V.M. Loktev, Phys. Rev. B 64, 134519 (2001).
92. This derivation (Refs. 8, 64, and 65) starts from an attractive pairing interaction, which is decoupled using a Hubbard-Stratonovich transformation. The decoupling field is the complex superconducting gap Δ. A gauge transformation of the fermions then removes the phase from Δ and couples it directly to the fermions. After the fermions are integrated out, one obtains the effective action of the phase.
93. G.D. Mahan, Many-Particle Physics, 2nd Ed. (Plenum, New York, 1990).
94. S. Wermbter and L. Tewordt, Physica C 211, 132 (1993).
95. S. Kamal, D.A. Bonn, N. Goldenfeld, P.J. Hirschfeld, R. Liang, and W.N. Hardy, Phys. Rev. Lett. 73, 1845 (1994); S. Kamal, R. Liang, A. Hosseini, D.A. Bonn, and W.N. Hardy, Phys. Rev. B 58, R8933 (1998).
96. S. Kamal, D.A. Bonn, N. Goldenfeld, P.J. Hirschfeld, R. Liang, and W.N. Hardy, Phys. Rev. Lett. 73, 1845 (1994); S. Kamal, R. Liang, A. Hosseini, D.A. Bonn, and W.N. Hardy, Phys. Rev. B 58, R8933 (1998).
97. D.A. Bonn and W.N. Hardy, in Physical Properties of High Temperature Superconductors, edited by D.M. Ginsburg. (World Scientific, Singapore, 1996), Vol. 5, p. 7.
98. 0.
99. c is small.
100. J.E. Mooij, in Percolation, Localization, and Superconductivity, edited by A.M. Goldman and S.A. Wolf (Plenum, New York, 1984), p. 325.
101. J. Adler, C. Holm, and W. Janke, Physica A 201, 58, (1993).
102. E. Babaev and H. Kleinert, Phys. Rev. B 59, 12 083 (1999); see also H. Kleinert, Phys. Rev. Lett. 84, 286 (2000).
103. E. Babaev and H. Kleinert, Phys. Rev. B 59, 12 083 (1999); see also H. Kleinert, Phys. Rev. Lett. 84, 286 (2000).
104. J.L. Tallon, C. Bernhard, H. Shaked, R.L. Hitterman, and J.D. Jorgensen, Phys. Rev. B 51, 12 911 (1995).
105. D.L. Feng, D.H. Lu, K.M. Shen, C. Kim, H. Eisaki, A. Damascelli, R. Yoshizaki, J.-I. Shimoyama, K. Kishio, G.D. Gu, S. Oh, A. Andrus, J. O'Donnell, J.N. Eckstein, and Z.-X. Shen, Science 289, 277 (2000).
106. C. Bernhard, J.L. Tallon, T. Blasius, A. Golnik, and C. Niedermayer, Phys. Rev. Lett. 86, 1614 (2001).
107. A. van Otterlo, D.S. Golubev, A.D. Zaikin, and G. Blatter, Eur. Phys. J. B 10, 131 (1999).
108. H. Monien, J. Low Temp. Phys. 126, 1123 (2002).
109. D.S. Marshall, D.S. Dessau, A.G. Loeser, C-H. Park, A.Y. Matsuura, J.N. Eckstein, I. Bozovic, P. Fournier, A. Kapitulnik, W.E. Spicer, and Z.-X. Shen, Phys. Rev. Lett. 76, 4841 (1996).
110. H. Ding, T. Yokoya, J.C. Campuzano, T. Takahashi, M. Randeria, M.R. Norman, T. Mochiku, K. Kadowaki, and J. Giapintzakis, Nature (London) 382, 51 (1996).
111. C. Timm (unpublished).
112. J. Bardeen and M.J. Stephen, Phys. Rev. 140, A1197 (1965).
113. D.S. Fisher, Phys. Rev. B 22, 1190 (1980).
114. C.T Rogers, K.E. Myers, J.N. Eckstein, and I. Bozovic, Phys. Rev. Lett. 69, 160 (1992).
115. 0/Θ)exp(2C/Θ).
116. S. Hensen, G. Müller, C.T Rieck, and K. Schamberg, Phys. Rev. B 56, 6237 (1997).