Superconductivity due to massless boson exchange in the strong-coupling limit

Physical Review B - Condensed Matter and Materials Physics

Volumn 72, Issue 17, 2005, Pages

  Chubukov, Andrey V ^a   Schmalian, Jörg ^b  

^a Bldg 142   (United States)

^b IOWA STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 29544435596     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.72.174520     Document Type: Article

References (79)

1. G. M. Eliashberg, Sov. Phys. JETP SPHJAR 0038-5646 11, 696 (1960);
2. G. M. Eliashberg, Sov. Phys. JETP SPHJAR 0038-5646 16, 780 (1963).
3. D. J. Scalapino, in Superconductivity, edited by, R. D. Parks, (Dekker, New York, 1969), Vol. 1, p. 449.
4. W. L. McMillan, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.167.331 167, 331 (1968).
5. F. Marsiglio and J. P. Carbotte, in The Physics of Superconductors, edited by, K. H. Bennemann, and, J. B. Ketterson, (Springer, Berlin, 2003), Vol. 1.
6. A. Migdal, Sov. Phys. JETP SPHJAR 0038-5646 7, 996 (1958).
7. V. J. Emery, Ann. Phys. (N.Y.) APNYA6 0003-4916 10.1006/aphy.2001.6135 28, 1 (1964).
8. N. F. Berk and J. R. Schrieffer, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.17.433 17, 433 (1966).
9. P. W. Anderson and R. F. Brinkman, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.30.1108 30, 1108 (1973).
10. P. W. Anderson and P. Morel, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.123.1911 123, 1911 (1961).
11. A. J. Leggett, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.47.331 47, 331 (1975).
12. V. J. Emery, Synth. Met. SYMEDZ 0379-6779 10.1016/0379-6779(86)90054-8 13, 21 (1986).
13. K. Miyake, S. Schmitt-Rink, and C. M. Varma, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.34.6554 34, 6554 (1986).
14. D. J. Scalapino, E. Loh, Jr., and J. E. Hirsch, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.34.8190 34, 8190 (1986).
15. P. Monthoux, A. V. Balatsky, and D. Pines, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.67.3448 67, 3448 (1991).
16. D. J. Scalapino, Phys. Rep. PRPLCM 0370-1573 10.1016/0370-1573(94)00086-I 250, 329 (1995).
17. P. Monthoux and D. Pines, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.69.961 69, 961 (1992).
18. D. Pines, Z. Phys. B: Condens. Matter ZPCMDN 0722-3277 10.1007/s002570050346 103, 129 (1997).
19. J. R. Schrieffer, J. Low Temp. Phys. JLTPAC 0022-2291 10.1007/BF00752315 99, 397 (1995).
20. A. V. Chubukov, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.52.R3840 52, R3840 (1995).
21. B. L. Altshuler, L. B. Ioffe, and A. J. Millis, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.52.5563 52, 5563 (1995).
22. Ar. Abanov, A. Chubukov, and A. Finkel'stein, Europhys. Lett. EULEEJ 0295-5075 10.1209/epl/i2001-00266-0 54, 488 (2001).
23. R. Roussev and A. J. Millis, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.63.140504 63, 140504 (R) (2001).
24. Z. Wang, W. Mao, and K. Bedell, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.87.257001 87, 257001 (2001).
25. M. Dzero and L. P. Gor'kov, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.69.092501 69, 092501 (2004).
26. A. Abanov, A. V. Chubukov, and J. Schmalian, Adv. Phys. ADPHAH 0001-8732 10.1080/0001873021000057123 52, 119 (2003);
27. A. V. Chubukov, D. Pines, and J. Schmalian, in The Physics of Superconductors, edited by, K. H. Bennemann, and, J. B. Ketterson, (Springer, Berlin, 2003), Vol. 1, p. 495.
28. A. Chubukov, A. Finkelstein, R. Haslinger, and D. Morr, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.90.077002 90, 077002 (2003).
29. A. V. Chubukov, V. M. Galitski, and V. M. Yakovenko, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.046404 94, 046404 (2005).
30. N. D. Mathur, F. M. Grosche, S. R. Julian, I. R. Walker, D. M. Freye, R. K. W. Haselwimmer, and G. G. Lonzarich, Nature (London) NATUAS 0028-0836 10.1038/27838 394, 39 (1998).
31. Y. Maeno, H. Hashimoto, K. Yoshida, S. Nishizaki, T. Fujita, J. G. Bednorz, and F. Lichtenberg, Nature (London) NATUAS 0028-0836 10.1038/372532a0 372, 532 (1994).
32. S. Saxena, P. Agarwal, K. Ahilan, F. Grosche, R. Haselwimmer, M. Steiner, E. Pugh, I. Walker, S. Julian, P. Monthoux, G. Lonzarich, A. Huxley, I. Sheikin, D. Braithwaite, and J. Flouquet, Nature (London) NATUAS 0028-0836 10.1038/27838 394, 39 (1998).
33. D. Aoki, A. Huxley, E. Ressouche, D. Braithwaite, J. Flouquet, J.-P. Brison, E. Lhotel, and C. Paulsen, Nature (London) NATUAS 0028-0836 10.1038/35098048 413, 61 (2001).
34. Z. Fisk and D. Pines, Nature (London) NATUAS 0028-0836 10.1038/27779 394, 22 (2001).
35. D. T. Son, Phys. Rev. D PRVDAQ 0556-2821 10.1103/PhysRevD.59.094019 59, 094019 (1999).
36. D. J. Gross and F. Wilczek, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.30.1343 30, 1343 (1973);
37. H. D. Polizer, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.30. 1346 30, 1346 (1973).
38. D. Bailin and A. Love, Phys. Rep. PRPLCM 0370-1573 10.1016/0370-1573(84) 90145-5 107, 325 (1984).
39. M. Alford, K. Rajagopal, and F. Wilczek, Phys. Lett. B PYLBAJ 0370-2693 10.1016/S0370-2693(98)00051-3 422, 247 (1998).
40. R. Rapp, T. Schafer, E. V. Shuryak, and M. Velkovsky, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.81.53 81, 53 (1998).
41. T. Schäfer and F. Wilczek, Phys. Rev. D PRVDAQ 0556-2821 10.1103/PhysRevD.60.114033 60, 114033 (1999).
42. R. D. Pisarski and D. H. Rischke, Phys. Rev. D PRVDAQ 0556-2821 10.1103/PhysRevD.61.051501 61, 051501 (R) (2000).
43. The condition g 1 near SDW or CDW instabilities can still be valid in some cases, but requires extra assumptions about the behavior of the interaction u(r) in real space (Ref.).
44. T. Holstein, R. E. Norton, and P. Pincus, Phys. Rev. B PLRBAQ 0556-2805 10.1103/PhysRevB.8.2649 8, 2649 (1973).
45. M. Yu. Reizer, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.40.11571 40, 11571 (1989).
46. R. Pisarski and D. Rischke, Nucl. Phys. A NUPABL 0375-9474 10.1016/S0375-9474(02)00702-9 702, 177 (2002).
47. J. Bardeen, L. N. Cooper, and J. R. Schrieffer, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.108.1175 108, 1175 (1957).
48. C. M. Varma, P. B. Littlewood, S. Schmitt-Rink, E. Abrahams, and A. E. Ruckenstein, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.63.1996 63, 1996 (1989).
49. P. B. Littlewood and C. M. Varma, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.46.405 46, 405 (1992).
50. Q. Wang and D. H. Rischke, Phys. Rev. D PRVDAQ 0556-2821 10.1103/PhysRevD.65.054005 65, 054005 (2002).
51. Physically, a finite Φ0 can be realized by coupling our system to another superconductor through a weak Josephson junction.
52. P. B. Allen and R. C. Dynes, Phys. Rev. B PLRBAQ 0556-2805 10.1103/PhysRevB.12.905 12, 905 (1975).
53. J. P. Carbotte, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.62. 1027 62, 1027 (1990).
54. F. Marsiglio and J. P. Carbotte, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.33.6141 33, 6141 (1986).
55. R. Combescot, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.51.11625 51, 11625 (1995).
56. V. L. Pokrovski, JETP Lett. JTPLA2 0021-3640 47, 629 (1988).
57. V. L. Emery and S. A. Kivelson, Nature (London) NATUAS 0028-0836 10.1038/374434a0 374, 434 (1995).
58. M. Franz and A. J. Millis, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.58.14572 58, 14572 (1999);
59. H. J. Kwon and A. T. Dorsey, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.59.6438 59, 6438 (1999).
60. A. V. Chubukov, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.72.085113 72, 085113 (2005).
61. The restriction to Ising systems is important as the transition becomes otherwise of first order (Ref.).
62. P. W. Anderson, Science SCIEAS 0036-8075 10.1016/S0921-4534(97)00266-9 235, 1196 (1987).
63. C. Gross, R. Joynt, and T. M. Rice, Z. Phys. B: Condens. Matter ZPCMDN 0722-3277 10.1007/BF01471072 68, 425 (1987);
64. C. Gros, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.38.931 38, 931 (1988).
65. A. Paramekanti, M. Randeria, and N. Trivedi, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.87.217002 87, 217002 (2001);
66. A. Paramekanti, M. Randeria, and N. Trivedi, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.70.054504 70, 054504 (2004).
67. J. Liu, J. Schmalian, and N. Trivedi, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.127003 94, 127003 (2005).
68. This result is consistent with the experimental observation (Ref.) that Tc in underdoped cuprates scales with the neutron peak frequency. Note in this regard that in quantum-critical, exciton scenario of the neutron peak (Refs.) the resonance peak frequency is Ωres∼(ΔωSF)1 2 where Δ is a gap, and ωSF is the spin-fluctuation frequency. At strong coupling, Δ∼ωSF∼t2 u∼J, and Ωres=O(J).
69. H. F. Fong, B. Keimer, D. Reznik, D. L. Milius, and I. A. Aksay, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.54.6708 54, 6708 (1996);
70. P. Dai, H. A. Mook, S. M. Hayden, G. Aeppli, T. G. Perring, D. Hunt, and F. Dogan, Science SCIEAS 0036-8075 10.1126/science.284.5418.1344 284, 1344 (1999);
71. H. F. Fong, P. Bourges, Y. Sidis, L. P. Regnault, J. Bossy, A. Ivanov, D. L. Milius, I. A. Aksay, and B. Keimer, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.61.14773 61, 14773 (2000).
72. M. R. Norman and H. Ding, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.57.R11089 57, R11089 (1998);
73. M. Eschrig and M. R. Norman, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.85.3261 85, 3261 (2000).
74. A. J. Leggett, in Modern Trends in the Theory of Condensed Matter, edited by, A. Pekalski, and, R. Przystawa, (Springer-Verlag, Berlin, 1980).
75. P. Nozieres and S. Schmitt-Rink, J. Low Temp. Phys. JLTPAC 0022-2291 10.1007/BF00683774 59, 195 (1985).
76. R. T. Scalettar, E. Y. Loh, J. E. Gubernatis, A. Moreo, S. R. White, D. J. Scalapino, R. L. Sugar, and E. Dagotto, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.62.1407 62, 1407 (1989).
77. C. A. R. Sa de Melo, M. Randeria, and J. R. Engelbrecht, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.71.3202 71, 3202 (1993).
78. Ar. Abanov, B. L. Altshuler, A. Chubukov, and E. Yuzbashyan (unpublished).
79. D. V. Khveshchenko and W. F. Shively, cond-mat/0510519 (unpublished).