- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Reviews of Modern Physics

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Impurity-induced states in conventional and unconventional superconductors

A. V. Balatsky*, I. Vekhter†, and Jian-Xin Zhu‡

A. V. Balatsky*

  • 1Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA

I. Vekhter†

  • 1Department of Physics and Astronomy, Louisiana State University, Baton Rouge, Louisiana 70803, USA

Jian-Xin Zhu‡

  • 1Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA

  • *Electronic address: avb@lanl.gov, http://theory.lanl.gov
  • †Electronic address: vekhter@phys.lsu.edu
  • ‡Electronic address: jxzhu@lanl.gov
PDF

Rev. Mod. Phys. 78, 373 – Published 9 May, 2006

DOI: https://doi.org/10.1103/RevModPhys.78.373

Abstract

This review presents recent developments in the understanding of how impurities influence the electronic states in the bulk properties of superconductors. The focus is on quasilocalized states in the vicinity of impurity sites in conventional and unconventional superconductors and the goal is to provide a unified framework for their description. The nonmagnetic impurity resonances in unconventional superconductors are directly related to the Yu-Shiba-Rusinov states around magnetic impurities in conventional s-wave systems. The physics behind these states, including the quantum phase transition between screened and unscreened impurities, are reviewed and recent work on d-wave superconductors is emphasized. The bound states are seen in scanning-tunneling spectroscopy measurements on high-Tc cuprates, which are described in detail. This paper discusses very recent progress in our understanding of states coupled to impurity sites, which have their own dynamics. Also reviewed are inelastic electron-tunneling spectroscopy features that could be seen by scanning-tunneling microscopy in real space and their Fourier-transformed images and impurity resonances in the presence of an order competing with superconductivity. The last part of the review is devoted to the influence of local deviations of the impurity concentration from its average value on the density of states in s-wave superconductors. Discussed is how these fluctuations affect the density of states and it is shown that s-wave superconductors are, strictly speaking, gapless in the presence of an arbitrarily small concentration of magnetic impurities.

View figure in article

Article Text

References (369)

  1. Abanov, A., and A. V. Chubukov, 2000, Phys. Rev. BPRBMDO10.1103/PhysRevB.61.R9241 61, R9241.
  2. Abanov, A., A. V. Chubukov, M. Eschrig, M. R. Norman, and J. Schmalian, 2002, Phys. Rev. Lett.PRLTAO10.1103/PhysRevLett.89.177002 89, 177002.
  3. Abrahams, E., and C. M. Varma, 2000, Proc. Natl. Acad. Sci. U.S.A.PNASA610.1073/pnas.100118797 97, 5714.
  4. Abrikosov, A. A., and L. P. Gor’kov, 1960, Zh. Eksp. Teor. Fiz.ZETFA7 39, 1781 [Sov. Phys. JETPSPHJAR 12, 1243 (1961)].
  5. Abrikosov, A. A., L. P. Gor’kov, and I. E. Dzyaloshinski, 1963, Methods of Quantum Field Theory in Statistical Physics (Dover, New York).
  6. Adagideli, I., P. M. Goldbart, A. Shnirman, and A. Yazdani, 1999, Phys. Rev. Lett.PRLTAO10.1103/PhysRevLett.83.5571 83, 5571.
  7. Affleck, I., and J. B. Marston, 1988, Phys. Rev. BPRBMDO10.1103/PhysRevB.37.3774 37, 3774.
  8. Alloul, H., P. Mendels, H. Casalta, J.-F. Marucco, and J. Arabski, 1991, Phys. Rev. Lett.PRLTAO10.1103/PhysRevLett.67.3140 67, 3140.
  9. Altland, A., B. D. Simons, and D. Taras-Semchuk, 2000, Adv. Phys.ADPHAH10.1080/000187300243354 49, 321.
  10. Altland, A., B. D. Simons, and M. R. Zirnbauer, 2002, Phys. Rep.PRPLCM10.1016/S0370-1573(01)00065-5 359, 283.
  11. Altland, A., and M. Zirnbauer, 1997, Phys. Rev. BPRBMDO10.1103/PhysRevB.55.1142 55, 1142.
  12. Altshuler, B. L., 1985, Pis'ma Zh. Eksp. Teor. Fiz.PZETAB 51, 530 [JETP Lett.JTPLA2 41, 648 (1985)].
  13. Ambegaokar, V., and A. Griffin, 1965, Phys. Rev.PRVAAH10.1103/PhysRev.137.A1151 137, A1151.
  14. Andersen, B. M., 2003, Phys. Rev. BPRBMDO10.1103/PhysRevB.68.094518 68, 094518.
  15. Andersen, B. M., and P. Hedegård, 2003, Phys. Rev. BPRBMDO10.1103/PhysRevB.67.172505 67, 172505.
  16. Andersen, O. K., A. I. Lichtenstein, O. Jepsen, and F. Paulsen, 1995, J. Phys. Chem. SolidsJPCSAW10.1016/0022-3697(95)00269-3 56, 1573.
  17. Anderson, P. W., 1959, Phys. Rev. Lett.PRLTAO10.1103/PhysRevLett.3.325 3, 325.
  18. Anderson, P. W., 1970, J. Phys. CJPSOAW10.1088/0022-3719/3/12/008 3, 2436.
  19. Anderson, P. W., G. Yuval, and D. R. Hamann, 1970, Phys. Rev. BPLRBAQ 1, 4464.10.1103/PhysRevB.1.4464
  20. Andrei, N., 1980, Phys. Rev. Lett.PRLTAO10.1103/PhysRevLett.45.379 45, 379.
  21. Annett, J., 1990, Adv. Phys.ADPHAH10.1080/00018739000101481 39, 83.
  22. Aprili, M., M. Covington, E. Paraoanu, B. Niedermeier, and L. H. Greene, 1998, Phys. Rev. BPRBMDO10.1103/PhysRevB.57.R8139 57, R8139.
  23. Arfi, B., H. Bahlouli, C. Pethick, and D. Pines, 1988, Phys. Rev. Lett.PRLTAO10.1103/PhysRevLett.60.2206 60, 2206.
  24. Aristov, D. N., and A. G. Yashenkin, 1998, Phys. Rev. Lett.PRLTAO10.1103/PhysRevLett.80.1116 80, 1116.
  25. Atkinson, W. A., and P. J. Hirschfeld, 2002, Phys. Rev. Lett.PRLTAO10.1103/PhysRevLett.88.187003 88, 187003.
  26. Atkinson, W. A., P. J. Hirschfeld, A. H. MacDonald, and K. Ziegler, 2000, Phys. Rev. Lett.PRLTAO10.1103/PhysRevLett.85.3926 85, 3926.
  27. Atkinson, W. A., P. J. Hirschfeld, and L. Zhu, 2003, Phys. Rev. BPRBMDO10.1103/PhysRevB.68.054501 68, 054501.
  28. Bader, S. D., N. E. Phillips, M. B. Maple, and C. A. Luengo, 1975, Solid State Commun.SSCOA410.1016/0038-1098(75)90161-1 16, 1263.
  29. Balatsky, A., 1998, Phys. Rev. Lett.PRLTAO10.1103/PhysRevLett.80.1972 80, 1972.
  30. Balatsky, A., 2000, Phys. Rev. BPRBMDO10.1103/PhysRevB.61.6940 61, 6940.
  31. Balatsky, A., and E. Abrahams, 1992, Phys. Rev. BPRBMDO10.1103/PhysRevB.45.13125 45, 13125.
  32. Balatsky, A. V., A. Abanov, and J.-X. Zhu, 2003, Phys. Rev. BPRBMDO10.1103/PhysRevB.68.214506 68, 214506.
  33. Balatsky, A. V., A. Rosengren, and B. L. Altshuler, 1994, Phys. Rev. Lett.PRLTAO10.1103/PhysRevLett.73.720 73, 720.
  34. Balatsky, A. V., and M. I. Salkola, 1998, Phys. Rev. Lett.PRLTAO10.1103/PhysRevLett.80.1117 80, 1117.
  35. Balatsky, A. V., M. I. Salkola, and A. Rosengren, 1995, Phys. Rev. BPRBMDO10.1103/PhysRevB.51.15547 51, 15547.
  36. Balatsky, A. V., and S. A. Trugman, 1997, Phys. Rev. Lett.PRLTAO10.1103/PhysRevLett.79.3767 79, 3767.
  37. Barash, Y. S., A. Grishin, and M. Sigrist, 1997, Zh. Eksp. Teor. Fiz.ZETFA7 112, 304 [JETPJTPHES10.1134/1.558301 85, 168 (1997)].
  38. Barash, Y. S., M. S. Kalenkov, and J. Kurkijrvi, 2000, Phys. Rev. BPRBMDO10.1103/PhysRevB.62.6665 62, 6665.
  39. Bauriedl, W., P. Ziemann, and W. Buckel, 1981, Phys. Rev. Lett.PRLTAO10.1103/PhysRevLett.47.1163 47, 1163.
  40. Beloborodov, I. S., B. N. Narozhny, and I. L. Aleiner, 2000, Phys. Rev. Lett.PRLTAO10.1103/PhysRevLett.85.816 85, 816.
  41. Berezinskii, V., 1974, Phys. Rev. Lett.PRLTAO 20, 628 [JETP Lett.JTPLA2 20, 287 (1974)].
  42. Berlinsky, A. J., D. A. Bonn, R. Harris, and C. Kallin, 2000, Phys. Rev. BPRBMDO10.1103/PhysRevB.61.9088 61, 9088.
  43. Bhaseen, M. J., J. S. Caux, I. I. Kogan, and A. M. Tsvelik, 2001, Nucl. Phys. BNUPBBO10.1016/S0550-3213(01)00432-1 618, 465.
  44. Bickers, N. E., and G. E. Zwicknagl, 1987, Phys. Rev. BPRBMDO10.1103/PhysRevB.36.6746 36, 6746.
  45. Blonder, G. E., M. Tinkham, and T. M. Klapwijk, 1982, Phys. Rev. BPRBMDO10.1103/PhysRevB.25.4515 25, 4515.
  46. Blount, E. I., 1985, Phys. Rev. BPRBMDO10.1103/PhysRevB.32.2935 32, 2935.
  47. Bobroff, J., H. Alloul, W. MacFarlane, P. Mendels, N. Blanchard, G. Collin, and J. Marucco, 2001, Phys. Rev. Lett.PRLTAO10.1103/PhysRevLett.86.4116 86, 4116.
  48. Borkowski, L. S., and P. J. Hirschfeld, 1992, Phys. Rev. BPRBMDO10.1103/PhysRevB.46.9274 46, 9274.
  49. Borkowski, L. S., and P. J. Hirschfeld, 1994, J. Low Temp. Phys.JLTPAC10.1007/BF00752405 96, 185.
  50. Brandt, U., 1970, J. Low Temp. Phys.JLTPAC10.1007/BF00628275 2, 573.
  51. Buchholtz, L. J., and G. Zwicknagl, 1981, Phys. Rev. BPRBMDO10.1103/PhysRevB.23.5788 23, 5788.
  52. Bulaevskii, L., V. Kuzii, and A. Sobyanin, 1977, Pis'ma Zh. Eksp. Teor. Fiz.PZETAB 25, 314 [JETP Lett.JTPLA2 25, 290 (1977)].
  53. Bulla, R., M. T. Glossop, D. E. Logan, and T. Pruschke, 2000, J. Phys.: Condens. MatterJCOMEL10.1088/0953-8984/12/23/302 12, 4899.
  54. Bulla, R., T. Pruschke, and A. C. Hewson, 1997, J. Phys.: Condens. MatterJCOMEL10.1088/0953-8984/9/47/014 9, 10463.
  55. Buzdin, A. I., 2005, Rev. Mod. Phys.RMPHAT10.1103/RevModPhys.77.935 77, 935.
  56. Buzdin, A., L. Bulaevskii, and S. Panyukov, 1982, J. Phys.: Condens. MatterJCOMEL 35, 147 [JETP Lett.JTPLA2 35, 178 (1982)].
  57. Byers, J. M., M. E. Flatté, and D. J. Scalapino, 1993, Phys. Rev. Lett.PRLTAO10.1103/PhysRevLett.71.3363 71, 3363.
  58. Campuzano, J. C., M. R. Norman, and M. Randeria, 2004, Physics of Superconductors (Springer, Berlin), Vol. II, p. 167.
  59. Campuzano, J. C., et al., 1999, Phys. Rev. Lett.PRLTAO10.1103/PhysRevLett.83.3709 83, 3709.
  60. Capriotti, L., D. J. Scalapino, and R. D. Sedgewick, 2003, Phys. Rev. BPRBMDO10.1103/PhysRevB.68.014508 68, 014508.
  61. Carbotte, J. P., 1990, Rev. Mod. Phys.RMPHAT10.1103/RevModPhys.62.1027 62, 1027.
  62. Carr, G. L., R. P. S. M. Lobo, J. LaVeigne, D. H. Reitze, and D. B. Tanner, 2000, Phys. Rev. Lett.PRLTAO10.1103/PhysRevLett.85.3001 85, 3001.
  63. Cassanello, C. R., and E. Fradkin, 1996, Phys. Rev. BPRBMDO10.1103/PhysRevB.53.15079 53, 15079.
  64. Cassanello, C. R., and E. Fradkin, 1997, Phys. Rev. BPRBMDO10.1103/PhysRevB.56.11246 56, 11246.
  65. Chaba, A. N., and A. D. S. Nagi, 1972, Can. J. Phys.CJPHAD 50, 1736.
  66. Chakravarty, S., R. B. Laughlin, D. K. Morr, and C. Nayak, 2001, Phys. Rev. BPRBMDO10.1103/PhysRevB.63.094503 63, 094503.
  67. Chamon, C., and C. Mudry, 2001, Phys. Rev. BPRBMDO10.1103/PhysRevB.63.100503 63, 100503.
  68. Chen, D. C., D. Rainer, and J. Sauls, 1998, in Proceedings of the International Conference on Quasiclassical Methods in Superconductivity and Superfluidity, Verditz 1996, edited by D. Rainer and J. A. Sauls (University Bayreuth, Bayreuth, Germany).
  69. Chen, H.-D., J.-P. Hu, S. Capponi, E. Arrigoni, and S.-C. Zhang, 2002, Phys. Rev. Lett.PRLTAO10.1103/PhysRevLett.89.137004 89, 137004.
  70. Chen, H. Y., and C. S. Ting, 2003, Phys. Rev. BPRBMDO10.1103/PhysRevB.68.212502 68, 212502.
  71. Chen, K., and C. Jayaprakash, 1995, J. Phys.: Condens. MatterJCOMEL10.1088/0953-8984/7/37/003 7, L491.
  72. Chen, Q., I. Kosztin, B. Janko, and K. Levin, 1998, Phys. Rev. Lett.PRLTAO10.1103/PhysRevLett.81.4708 81, 4708.
  73. Chen, Y., and C. S. Ting, 2004, Phys. Rev. Lett.PRLTAO10.1103/PhysRevLett.92.077203 92, 077203.
  74. Chiao, M., R. W. Hill, C. Lupien, L. Taillefer, P. Lambert, R. Gagnon, and P. Fournier, 2000, Phys. Rev. BPRBMDO10.1103/PhysRevB.62.3554 62, 3554.
  75. Choi, C., and P. Muzikar, 1990, Phys. Rev. BPRBMDO10.1103/PhysRevB.41.1812 41, 1812.
  76. Choi, C. H., 1999, Phys. Rev. BPRBMDO10.1103/PhysRevB.60.6884 60, 6884.
  77. Chubukov, A. V., A. Abanov, and D. N. Basov, 2003, Phys. Rev. BPRBMDO10.1103/PhysRevB.68.024504 68, 024504.
  78. Coleman, P., 1984, Phys. Rev. BPRBMDO10.1103/PhysRevB.29.3035 29, 3035.
  79. Coleman, P., 1985, J. Magn. Magn. Mater.JMMMDC 47, 323.
  80. Corson, J., J. Orenstein, S. Oh, J. O’Donnell, and J. N. Eckstein, 2000, Phys. Rev. Lett.PRLTAO10.1103/PhysRevLett.85.2569 85, 2569.
  81. Covington, M., M. Aprili, E. Paraoanu, L. H. Greene, F. Xu, J. Zhu, and C. A. Mirkin, 1997, Phys. Rev. Lett.PRLTAO10.1103/PhysRevLett.79.277 79, 277; PRLTAO10.1103/PhysRevLett.79.259879, 2598(E) (1997).
  82. Cox, D. L., and A. Zawadowski, 1998, Adv. Phys.ADPHAH10.1080/000187398243500 47, 599.
  83. Damascelli, A., Z. Hussain, and Z.-X. Shen, 2003, Rev. Mod. Phys.RMPHAT10.1103/RevModPhys.75.473 75, 473.
  84. de Gennes, P. G., 1989, Superconductivity of Metals and Alloys (Addison-Wesley, New York).
  85. Dessau, D. S., B. O. Wells, Z. Shen, W. E. Spicer, A. J. Arko, R. S. List, D. B. Mitzi, and A. Kapitulnik, 1991, Phys. Rev. Lett.PRLTAO10.1103/PhysRevLett.66.2160 66, 2160.
  86. Duffy, D., P. J. Hirschfeld, and D. J. Scalapino, 2001, Phys. Rev. BPRBMDO10.1103/PhysRevB.64.224522 64, 224522.
  87. Dumoulin, L., E. Guyon, and P. Nedellec, 1975, Phys. Rev. Lett.PRLTAO10.1103/PhysRevLett.34.264 34, 264.
  88. Dumoulin, L., E. Guyon, and P. Nedellec, 1977, Phys. Rev. BPLRBAQ 16, 1086.10.1103/PhysRevB.16.1086
  89. Edelstein, A. S., 1967, Phys. Rev. Lett.PRLTAO10.1103/PhysRevLett.19.1184 19, 1184.
  90. Elliott, R. J., 1954, Phys. Rev.PHRVAO10.1103/PhysRev.96.266 96, 266.
  91. Emery, V. J., and S. A. Kivelson, 1995, Nature (London)NATUAS10.1038/374434a0 374, 434.
  92. Eschrig, M., and M. R. Norman, 2000, Phys. Rev. Lett.PRLTAO10.1103/PhysRevLett.85.3261 85, 3261.
  93. Fetter, A. L., 1965, Phys. Rev.PRVAAH10.1103/PhysRev.140.A1921 140, A1921.
  94. Fetter, A. L., and J. D. Walecka, 1971, Quantum Theory of Many-Particle Systems (McGraw-Hill, New York).
  95. Fischer, O., M. Kugler, I. Maggio-Aprile, C. Berthod, and C. Renner, 2005, Rev. Mod. Phys. (unpublished).
  96. Flatté, M. E., and J. M. Byers, 1997a, Phys. Rev. Lett.PRLTAO 78, 3761.
  97. Flatté, M. E., and J. M. Byers, 1997b, Phys. Rev. BPRBMDO 56, 11213.
  98. Flatte, M. E., and J. M. Byers, 1998, Phys. Rev. Lett.PRLTAO10.1103/PhysRevLett.80.4546 80, 4546.
  99. Flatté, M. E., and J. M. Byers, 1999, Solid State Phys.SSPHAE 52, 137.
  100. Fogelström, M., D. Rainer, and J. A. Sauls, 1997, Phys. Rev. Lett.PRLTAO10.1103/PhysRevLett.79.281 79, 281.
  101. Franz, M., C. Kallin, and A. J. Berlinsky, 1996, Phys. Rev. BPRBMDO10.1103/PhysRevB.54.R6897 54, R6897.
  102. Franz, M., D. E. Sheehy, and Z. Tešanović, 2002, Phys. Rev. Lett.PRLTAO10.1103/PhysRevLett.88.257005 88, 257005.
  103. Franz, M., and Z. Tešanović, 1998, Phys. Rev. Lett.PRLTAO10.1103/PhysRevLett.80.4763 80, 4763.
  104. Galitskii, V. M., and A. I. Larkin, 2002, Phys. Rev. BPRBMDO10.1103/PhysRevB.66.064526 66, 064526.
  105. Ghosal, A., and H. Y. Kee, 2004, Phys. Rev. BPRBMDO10.1103/PhysRevB.69.224513 69, 224513.
  106. Ghosal, A., M. Randeria, and N. Trivedi, 1998, Phys. Rev. Lett.PRLTAO10.1103/PhysRevLett.81.3940 81, 3940.
  107. Ginzberg, D. M., 1979, Phys. Rev. BPRBMDO10.1103/PhysRevB.20.960 20, 960.
  108. Glazman, L., and K. Matveev, 1989, Pis'ma Zh. Eksp. Teor. Fiz.PZETAB 49, 570 [JETP Lett.JTPLA2 49, 660 (1989)].
  109. Golubov, A. A., and I. I. Mazin, 1999, Phys. Rev. BPRBMDO 55, 15146.
  110. Gong, C.-D., and J.-H. Cai, 1966, J. Phys., (China) 22, 381.
  111. Gonzalez-Buxton, C., and K. Ingersent, 1998, Phys. Rev. BPRBMDO 57, 15254.
  112. Gor’kov, L. P., and P. A. Kalugin, 1985, Pis'ma Zh. Eksp. Teor. Fiz.PZETAB 41, 208 [JETP Lett.JTPLA2 41, 253 (1985)].
  113. Graf, M., A. Balatsky, and J. Sauls, 2000, Phys. Rev. BPRBMDO10.1103/PhysRevB.61.3255 61, 3255.
  114. Graf, M. J., J. Sauls, and D. Rainer, 1995, Phys. Rev. BPRBMDO10.1103/PhysRevB.52.10588 52, 10588.
  115. Graf, M. J., S.-K. Yip, J. A. Sauls, and D. Rainer, 1996, Phys. Rev. BPRBMDO10.1103/PhysRevB.53.15147 53, 15147.
  116. Grimaldi, C., 1999, Europhys. Lett.EULEEJ10.1209/epl/i1999-00482-6 48, 306.
  117. Grimaldi, C., 2002, Phys. Rev. BPRBMDO10.1103/PhysRevB.65.094502 65, 094502.
  118. Gweon, G.-H., T. Sasagawa, S. Y. Zhou, J. Graf, H. Takagi, D.-H. Lee, and A. Lanzara, 2004, Nature (London)NATUAS10.1038/nature02731 430, 187.
  119. Hahn, J. R., and W. Ho, 2001, Phys. Rev. Lett.PRLTAO10.1103/PhysRevLett.87.166102 87, 166102.
  120. Halperin, B. I., and M. Lax, 1966, Phys. Rev.PHRVAO10.1103/PhysRev.148.722 148, 722.
  121. Hamann, D. R., 1967, Phys. Rev.PHRVAO10.1103/PhysRev.158.570 158, 570.
  122. Han, Q., Z. D. Wang, X.-G. Li, and L. Y. Zhang, 2002, Phys. Rev. BPRBMDO10.1103/PhysRevB.66.104502 66, 104502.
  123. Han, Q., T. Xia, Z. D. Wang, and X.-G. Li, 2004, Phys. Rev. BPRBMDO10.1103/PhysRevB.69.224512 69, 224512.
  124. Haran, G., and A. D. S. Nagi, 1996, Phys. Rev. BPRBMDO10.1103/PhysRevB.54.15463 54, 15463.
  125. Haran, G., and A. D. S. Nagi, 1998, Phys. Rev. BPRBMDO10.1103/PhysRevB.58.12441 58, 12441.
  126. Harlingen, D. J. V., 1995, Rev. Mod. Phys.RMPHAT10.1103/RevModPhys.67.515 67, 515.
  127. Heinrichs, J., 1968, Phys. Rev.PHRVAO10.1103/PhysRev.168.451 168, 451.
  128. Hettler, M. H., and P. J. Hirschfeld, 1999, Phys. Rev. BPRBMDO10.1103/PhysRevB.59.9606 59, 9606.
  129. Hewson, A. C., 1993, The Kondo Problem to Heavy Fermions (Cambridge University Press, Cambridge).
  130. Hill, R. W., C. Lupien, M. Sutherland, E. Boaknin, D. G. Hawthorn, C. Proust, F. Ronning, L. Taillefer, R. Liang, D. A. Bonn, and W. N. Hardy, 2004, Phys. Rev. Lett.PRLTAO10.1103/PhysRevLett.92.027001 92, 027001.
  131. Hirschfeld, P. J., and W. A. Atkinson, 2002, J. Low Temp. Phys.JLTPAC10.1023/A:1013838523587 126, 881.
  132. Hirschfeld, P. J., and N. Goldenfeld, 1993, Phys. Rev. BPRBMDO10.1103/PhysRevB.48.4219 48, 4219.
  133. Hirschfeld, P. J., W. O. Putikka, and D. J. Scalapino, 1994, Phys. Rev. BPRBMDO10.1103/PhysRevB.50.10250 50, 10250.
  134. Hirschfeld, P. J., S. M. Quinlan, and D. J. Scalapino, 1997, Phys. Rev. BPRBMDO10.1103/PhysRevB.55.12742 55, 12742.
  135. Hirschfeld, P. J., P. Wölfle, D. Einzel, J. A. Sauls, and W. O. Putikka, 1989, Phys. Rev. BPRBMDO10.1103/PhysRevB.40.6695 40, 6695.
  136. Hirschfeld, P. J., P. Wölfle, and D. Vollhard, 1986, Solid State Commun.SSCOA410.1016/0038-1098(86)90190-0 59, 111.
  137. Hirschfeld, P. J., P. W. Wölfle, and D. Einzel, 1988, Phys. Rev. BPRBMDO10.1103/PhysRevB.37.83 37, 83.
  138. Hoffman, J. E., E. W. Hudson, K. M. Lang, V. Madhavan, H. Eisaki, S. Uchida, and J. C. Davis, 2002, ScienceSCIEAS10.1126/science.1066974 295, 466.
  139. Hoffman, J. E., K. McElroy, D.-H. Lee, K. M. Lang, H. Eisaki, S. Uchida, and J. C. Davis, 2002, ScienceSCIEAS10.1126/science.1072640 297, 1148.
  140. Hosseini, A., R. Harris, S. Kamal, P. Dosanjh, J. Preston, R. Liang, W. N. Hardy, and D. A. Bonn, 1999, Phys. Rev. BPRBMDO10.1103/PhysRevB.60.1349 60, 1349.
  141. Hotta, T., 1993, J. Phys. Soc. Jpn.JUPSAU10.1143/JPSJ.62.274 62, 274.
  142. Howald, C., H. Eisaki, N. Kaneko, M. Greven, and A. Kapitulnik, 2003, Phys. Rev. BPRBMDO10.1103/PhysRevB.67.014533 67, 014533.
  143. Howald, C., P. Fournier, and A. Kapitulnik, 2001, Phys. Rev. BPRBMDO10.1103/PhysRevB.64.100504 64, 100504.
  144. Howell, P. C., A. Rosch, and P. J. Hirschfeld, 2004, Phys. Rev. Lett.PRLTAO10.1103/PhysRevLett.92.037003 92, 037003.
  145. Hsu, T. C., J. B. Marston, and I. Affleck, 1991, Phys. Rev. BPRBMDO10.1103/PhysRevB.43.2866 43, 2866.
  146. Hu, C.-R., 1994, Phys. Rev. Lett.PRLTAO10.1103/PhysRevLett.72.1526 72, 1526.
  147. Hudson, E. W., K. M. Lang, V. Madhavan, S. H. Pan, H. Eisaki, S. Uchida, and J. C. Davis, 2001, Nature (London)NATUAS10.1038/35082019 411, 920.
  148. Hudson, E. W., S. H. Pan, A. K. Gupta, K.-W. Ng, and J. C. Davis, 1999, ScienceSCIEAS10.1126/science.285.5424.88 285, 88.
  149. Hussey, N. E., 2002, Adv. Phys.ADPHAH10.1080/00018730210164638 51, 1685.
  150. Ingersent, K., 1996, Phys. Rev. BPRBMDO10.1103/PhysRevB.54.11936 54, 11936.
  151. Ingersent, K., and Q. Si, 1998, e-print cond-mat/9810226.
  152. Ishida, K., Y. Kitaoka, N. Ogata, T. Kamino, K. Asayama, J. R. Cooper, and N. Athanassopoulou, 1993, J. Phys. Soc. Jpn.JUPSAU 63, 2803.
  153. Ishida, K., Y. Kitaoka, K. Yamazoe, K. Asayama, and Y. Yamada, 1996, Phys. Rev. Lett.PRLTAO10.1103/PhysRevLett.76.531 76, 531.
  154. Ishida, K., Y. Kitaoka, T. Yoshitomi, N. Ogata, T. Kamino, and K. Asayama, 1991, Physica CPHYCE610.1016/0921-4534(91)90007-L 179, 29.
  155. Itoh, Y., 1993, J. Phys. Soc. Jpn.JUPSAU10.1143/JPSJ.62.2184 62, 2184.
  156. Janko, B., I. Kosztin, K. Levin, M. Norman, and D. Scalapino, 1999, Phys. Rev. Lett.PRLTAO10.1103/PhysRevLett.82.4304 82, 4304.
  157. Jarrell, M., 1990, Phys. Rev. BPRBMDO10.1103/PhysRevB.41.4815 41, 4815.
  158. Jarrell, M., D. S. Silva, and B. Patton, 1990, Phys. Rev. BPRBMDO10.1103/PhysRevB.42.4804 42, 4804.
  159. Joynt, R., 1997, J. Low Temp. Phys.JLTPAC 109, 811.
  160. Kampf, A. P., and T. P. Devereaux, 1997, Phys. Rev. BPRBMDO10.1103/PhysRevB.56.2360 56, 2360.
  161. Kashiwaya, S., and Y. Tanaka, 2000, Rep. Prog. Phys.RPPHAG10.1088/0034-4885/63/10/202 63, 1641.
  162. Kee, H. Y., 2001, Phys. Rev. BPRBMDO10.1103/PhysRevB.64.012506 64, 012506.
  163. Kee, H.-Y., S. A. Kivelson, and G. Aeppli, 2002, Phys. Rev. Lett.PRLTAO10.1103/PhysRevLett.88.257002 88, 257002.
  164. Ketterson, J. B., and S. N. Song, 1999, Superconductivity (Cambridge University Press, Cambridge).
  165. Khaykovich, B., Y. S. Lee, R. W. Erwin, S. H. Lee, S. Wakimoto, K. J. Thomas, M. A. Kastner, and R. J. Birgeneau, 2002, Phys. Rev. BPRBMDO10.1103/PhysRevB.66.014528 66, 014528.
  166. Kim, H., and P. Muzikar, 1993, Phys. Rev. BPRBMDO 48, 39332.
  167. Kivelson, S. A., I. P. Bindloss, E. Fradkin, V. Oganesyan, J. M. Tranquada, A. Kapitulnik, and C. Howald, 2003, Rev. Mod. Phys.RMPHAT10.1103/RevModPhys.75.1201 75, 1201.
  168. Koga, M., and M. Matsumoto, 2002a, J. Phys. Soc. Jpn.JUPSAU 71, 943.
  169. Koga, M., and M. Matsumoto, 2002b, Phys. Rev. BPRBMDO 65, 094434.
  170. Kondo, J., 1964, Prog. Theor. Phys.PTPKAV10.1143/PTP.32.37 32, 37.
  171. Kosterlitz, J. M., and D. J. Thouless, 1973, J. Phys. CJPSOAW10.1088/0022-3719/6/7/010 6, 1181.
  172. Kosterlitz, J. M., and D. J. Thouless, 1974, J. Phys. CJPSOAW10.1088/0022-3719/7/6/005 7, 1046.
  173. Krasnov, V. M., A. Yurgens, D. Winkler, P. Delsing, and T. Claeson, 2000, Phys. Rev. Lett.PRLTAO10.1103/PhysRevLett.84.5860 84, 5860.
  174. Kruis, H. V., I. Martin, and A. V. Balatsky, 2001, Phys. Rev. BPRBMDO10.1103/PhysRevB.64.054501 64, 054501.
  175. Kuboki, K., and M. Sigrist, 1998, J. Phys. Soc. Jpn.JUPSAU10.1143/JPSJ.67.2873 67, 2873.
  176. Kulic, M. L., and O. V. Dolgov, 1999, Phys. Rev. BPRBMDO10.1103/PhysRevB.60.13062 60, 13062.
  177. Kulik, I. O., and O. Y. Itskovich, 1968, Zh. Eksp. Teor. Fiz.ZETFA7 55, 193 [Sov. Phys. JETPSPHJAR 28, 102 (1969)].
  178. Lake, B., G. Aeppli, K. N. Clause, D. F. McMorrow, K. Lefmann, N. E. Hussey, N. Mangkorntong, M. Nohara, H. Takagi, T. E. Mason, and A. Schröder, 2001, ScienceSCIEAS10.1126/science.1056986 291, 1759.
  179. Lake, B., et al., 2002, Nature (London)NATUAS10.1038/415299a 415, 299.
  180. Lamacraft, A., and B. D. Simons, 2000, Phys. Rev. Lett.PRLTAO10.1103/PhysRevLett.85.4783 85, 4783.
  181. Lamacraft, A., and B. D. Simons, 2001, Phys. Rev. BPRBMDO10.1103/PhysRevB.64.014514 64, 014514.
  182. Landau, L., and E. Lifshitz, 2000, Quantum Mechanics (Butterworth-Heinemann, Oxford), Vol. 3.
  183. Lang, K. M., V. Madhavan, J. E. Hoffman, E. W. Hudson, H. Eisaki, S. Uchida, and J. C. Davis, 2002, Nature (London)NATUAS10.1038/415412a 415, 412.
  184. Lanzara, A., et al., 2004, Nature (London)NATUAS10.1038/nature02731 430, 187.
  185. Larkin, A., 1965, JETP Lett.JTPLA2 2, 130.
  186. Larkin, A. I., V. I. Mel’nikov, and D. E. Khmelnitskii, 1971, Sov. Phys. JETPSPHJAR 33, 458.
  187. Larkin, A. I., and Y. N. Ovchinnikov, 1972, Sov. Phys. JETPSPHJAR 34, 1144.
  188. Laughlin, R. B., 1998, Phys. Rev. Lett.PRLTAO10.1103/PhysRevLett.80.5188 80, 5188.
  189. Lee, P. A., 1993, Phys. Rev. Lett.PRLTAO10.1103/PhysRevLett.71.1887 71, 1887.
  190. Lee, P. A., and T. V. Ramakrishnan, 1985, Rev. Mod. Phys.RMPHAT10.1103/RevModPhys.57.287 57, 287.
  191. Lee, Y.-S., K. Segawa, Y. Ando, and D. N. Basov, 2004, Phys. Rev. BPRBMDO10.1103/PhysRevB.70.014518 70, 014518.
  192. Li, J.-X., W.-G. Yin, and C.-D. Gong, 1998, Phys. Rev. BPRBMDO10.1103/PhysRevB.58.2895 58, 2895.
  193. Liang, S. D., and T. K. Lee, 2002, Phys. Rev. BPRBMDO10.1103/PhysRevB.65.214529 65, 214529.
  194. Lifshitz, I. M., 1964a, Adv. Phys.ADPHAH 13, 483.
  195. Lifshitz, I. M., 1964b, Usp. Fiz. NaukUFNAAG 83, 617 [Sov. Phys. Usp.SOPUAP10.1070/PU1965v007n04ABEH003634 7, 549 (1965)].
  196. Lifshitz, I. M., 1967, Zh. Eksp. Teor. Fiz.ZETFA7 53, 743 [Sov. Phys. JETPSPHJAR 26, 462 (1968)].
  197. Lifshitz, I. M., S. A. Gredeskul, and L. A. Pastur, 1988, Introduction to the Theory of Disordered Systems (Wiley, New York).
  198. Logan, D. E., and M. T. Glossop, 2000, J. Phys.: Condens. MatterJCOMEL10.1088/0953-8984/12/6/320 12, 985.
  199. Loktev, V. M., and Y. Pogorelov, 2002, Europhys. Lett.EULEEJ10.1209/epl/i2002-00373-4 60, 757.
  200. Loram, J. W., J. L. Luo, J. R. Cooper, W. Y. Liang, and J. L. Tallon, 2000, Physica CPHYCE6 341-348, 831.
  201. Ma, M., and P. A. Lee, 1985, Phys. Rev. BPRBMDO10.1103/PhysRevB.32.5658 32, 5658.
  202. Machida, K., and F. Shibata, 1972, Prog. Theor. Phys.PTPKAV10.1143/PTP.47.1817 47, 1817.
  203. Mackenzie, A. P., K. Haselwimmer, A. Tyler, G. Lonzarich, Y. Mori, S. Nishizaki, and Y. Maeno, 1998, Phys. Rev. Lett.PRLTAO10.1103/PhysRevLett.80.161 80, 161.
  204. Mackenzie, A. P., and Y. Maeno, 2003, Rev. Mod. Phys.RMPHAT10.1103/RevModPhys.75.657 75, 657.
  205. Mahajan, A. V., H. Alloul, G. Collin, and J.-F. Marucco, 1994, Phys. Rev. Lett.PRLTAO10.1103/PhysRevLett.72.3100 72, 3100.
  206. Mahajan, A. V., H. Alloul, G. Collin, and J.-F. Marucco, 2000, Eur. Phys. J. BEPJBFY 13, 457.
  207. Mahan, G. D., 2000, Many-Particle Physics, 3rd ed. (Kluwer Academic/Plenum, New York).
  208. Maki, K., 1969, in Superconductivity, edited by R. D. Parks (Dekker, New York), p. 1035.
  209. Maple, M. B., 1973, in Magnetism, edited by H. Suhl (Academic, New York), Vol. V, p. 289.
  210. Marchetti, F. M., and B. D. Simons, 2002, J. Phys. AJPHAC510.1088/0305-4470/35/19/302 35, 4201.
  211. Markowitz, D., and L. P. Kadanoff, 1963, Phys. Rev.PHRVAO10.1103/PhysRev.131.563 131, 563.
  212. Marston, J. B., and I. Affleck, 1989, Phys. Rev. BPRBMDO10.1103/PhysRevB.39.11538 39, 11538.
  213. Martin, I., and A. V. Balatsky, 2000, Phys. Rev. BPRBMDO 62, 6124.
  214. Martin, I., A. V. Balatsky, and J. Zaanen, 2002, Phys. Rev. Lett.PRLTAO10.1103/PhysRevLett.88.097003 88, 097003.
  215. Martinez-Samper, P., H. Suderow, S. Vieira, J. P. Brison, N. Luchier, P. Lejay, and P. C. Canfield, 2003, Phys. Rev. BPRBMDO10.1103/PhysRevB.67.014526 67, 014526.
  216. Matsumoto, M., and M. Koga, 2002, Phys. Rev. BPRBMDO 65, 024508.
  217. Matsuura, T., 1977, Prog. Theor. Phys.PTPKAV10.1143/PTP.57.1823 57, 1823.
  218. Matsuura, T., S. Ichinose, and Y. Nagaoka, 1977, Prog. Theor. Phys.PTPKAV10.1143/PTP.57.713 57, 713.
  219. McElroy, K., R. W. Simmonds, J. E. Hoffman, D. H. Lee, J. Orenstein, H. Eisaki, S. Uchida, and J. C. Davis, 2003, Nature (London)NATUAS10.1038/nature01496 422, 592.
  220. Mendels, P., J. Bobroff, G. Collin, H. Alloul, M. Gabay, J.-F. Marucco, N. Blanchard, and B. Grenier, 1999, Europhys. Lett.EULEEJ10.1209/epl/i1999-00319-x 46, 678.
  221. Meyer, J. S., and B. D. Simons, 2001, Phys. Rev. BPRBMDO10.1103/PhysRevB.64.134516 64, 134516.
  222. Millis, A. J., 2003, Solid State Commun.SSCOA410.1016/S0038-1098(02)00668-3 126, 3.
  223. Misra, S., S. Oh, D. J. Hornbaker, T. DiLuccio, J. N. Eckstein, and A. Yazdani, 2002, Phys. Rev. Lett.PRLTAO10.1103/PhysRevLett.89.087002 89, 087002.
  224. Moradian, R., J. F. Annett, B. L. Gyorffy, and G. Litak, 2001, Phys. Rev. BPRBMDO 63, 024501.
  225. Morr, D. K., 2002, Phys. Rev. Lett.PRLTAO10.1103/PhysRevLett.89.106401 89, 106401.
  226. Morr, D. K., and A. V. Balatsky, 2003, Phys. Rev. Lett.PRLTAO10.1103/PhysRevLett.90.067005 90, 067005.
  227. Morr, D. K., and R. H. Nyberg, 2003, Phys. Rev. BPRBMDO10.1103/PhysRevB.68.060505 68, 060505.
  228. Morr, D. K., and N. A. Stavropoulos, 2002, Phys. Rev. BPRBMDO10.1103/PhysRevB.66.140508 66, 140508.
  229. Morr, D. K., and N. A. Stavropoulos, 2003a, Phys. Rev. BPRBMDO 68, 094518.
  230. Morr, D. K., and N. A. Stavropoulos, 2003b, Phys. Rev. BPRBMDO 67, 020502.
  231. Movshovich, R., M. A. Hubbard, M. B. Salamon, A. V. Balatsky, R. Yoshizaki, J. L. Sarrao, and M. Jaime, 1998, Phys. Rev. Lett.PRLTAO10.1103/PhysRevLett.80.1968 80, 1968.
  232. Müller-Hartmann, E., 1973, in Magnetism, edited by H. Suhl (Academic, New York), Vol. V, p. 353.
  233. Müller-Hartmann, E., and J. Zittartz, 1971, Phys. Rev. Lett.PRLTAO10.1103/PhysRevLett.26.428 26, 428.
  234. Nagaoka, Y., 1965, Phys. Rev.PRVAAH10.1103/PhysRev.138.A1112 138, A1112.
  235. Nagaoka, Y., 1967, Prog. Theor. Phys.PTPKAV10.1143/PTP.37.13 37, 13.
  236. Neils, W. K., and D. J. V. Harlingen, 2002, Phys. Rev. Lett.PRLTAO10.1103/PhysRevLett.88.047001 88, 047001.
  237. Nersesyan, A., and A. Tsvelik, 1997, Phys. Rev. Lett.PRLTAO10.1103/PhysRevLett.78.3981 78, 3981.
  238. Nersesyan, A., A. Tsvelik, and F. Wenger, 1995, Nucl. Phys. BNUPBBO10.1016/0550-3213(95)00002-A 438, 561.
  239. Nicol, E. J., and J. P. Carbotte, 2003, Phys. Rev. BPRBMDO10.1103/PhysRevB.67.214506 67, 214506.
  240. Norman, M. R., and H. Ding, 1998, Phys. Rev. BPRBMDO 57, 11089.
  241. Norman, M. R., H. Ding, M. Randeria, J. C. Campuzano, T. Yokoya, T. Takeuchi, T. Takahashi, T. Mochiku, K. Kadowaki, P. Guptasarma, and D. G. Hinks, 1998, Nature (London)NATUAS10.1038/32366 392, 157.
  242. Norman, M. R., M. Randeria, H. Ding, and J. C. Campuzano, 1995, Phys. Rev. BPRBMDO10.1103/PhysRevB.52.615 52, 615.
  243. Ogura, J., and T. Saso, 1993, J. Phys. Soc. Jpn.JUPSAU10.1143/JPSJ.62.4364 62, 4364.
  244. Okabe, Y., and A. D. S. Nagi, 1983, Phys. Rev. BPRBMDO10.1103/PhysRevB.28.1320 28, 1320.
  245. Pan, S., E. W. Hudson, and J. Davis, 1998, Appl. Phys. Lett.APPLAB10.1063/1.122654 73, 2992.
  246. Pan, S. H., E. W. Hudson, A. K. Gupta, K.-W. Ng, H. Eisaki, S. Uchida, and J. C. Davis, 2000, Phys. Rev. Lett.PRLTAO10.1103/PhysRevLett.85.1536 85, 1536.
  247. Pan, S. H., E. W. Hudson, K. M. Lang, H. Eisaki, S. Uchida, and J. C. Davis, 2000, Nature (London)NATUAS 403, 746.
  248. Pan, S. H., et al., 2001, Nature (London)NATUAS10.1038/35095012 413, 282.
  249. Pepin, C., and P. A. Lee, 1998, Phys. Rev. Lett.PRLTAO10.1103/PhysRevLett.81.2779 81, 2779.
  250. Pepin, C., and P. A. Lee, 2001, Phys. Rev. BPRBMDO10.1103/PhysRevB.63.054502 63, 054502.
  251. Petersen, L., P. T. Sprunger, P. Hoffmann, E. Lægsgaard, B. G. Briner, M. Doering, H.-P. Rust, A. M. Bradshaw, F. Besenbacher, and E. W. Plummer, 1998, Phys. Rev. BPRBMDO10.1103/PhysRevB.57.R6858 57, R6858.
  252. Pethick, C. J., and D. Pines, 1986, Phys. Rev. Lett.PRLTAO10.1103/PhysRevLett.57.118 57, 118.
  253. Podolsky, D., E. Demler, K. Damle, and B. I. Halperin, 2003, Phys. Rev. BPRBMDO10.1103/PhysRevB.67.094514 67, 094514.
  254. Pogorelov, Y., 1994, Physica CPHYCE6 235-240, 2279.
  255. Polkovnikov, A., 2002, Phys. Rev. BPRBMDO10.1103/PhysRevB.65.064503 65, 064503.
  256. Polkovnikov, A., S. Sachdev, and M. Vojta, 2001, Phys. Rev. Lett.PRLTAO10.1103/PhysRevLett.86.296 86, 296.
  257. Polkovnikov, A., S. Sachdev, and M. Vojta, 2003, Physica CPHYCE6 388-389, 19.
  258. Quinlan, S. M., P. J. Hirschfeld, and D. J. Scalapino, 1996, Phys. Rev. BPRBMDO10.1103/PhysRevB.53.8575 53, 8575.
  259. Quinlan, S. M., D. J. Scalapino, and N. Bulut, 1994, Phys. Rev. BPRBMDO10.1103/PhysRevB.49.1470 49, 1470.
  260. Rainer, D., and M. Vuorio, 1977, J. Phys. CJPSOAW10.1088/0022-3719/10/16/018 10, 3093.
  261. Read, N., 1985, J. Phys. CJPSOAW10.1088/0022-3719/18/13/012 18, 2651.
  262. Read, N., and D. M. Newns, 1983a, J. Phys. CJPSOAW 16, 3273.
  263. Read, N., and D. M. Newns, 1983b, J. Phys. CJPSOAW 16, L1055.
  264. Renner, C., B. Revaz, J.-Y. Genoud, K. Kadowaki, and Ø. Fischer, 1998, Phys. Rev. Lett.PRLTAO10.1103/PhysRevLett.80.149 80, 149.
  265. Rusinov, A. I., 1968, Zh. Eksp. Teor. Fiz. Pis'ma Red.ZFPRAU 9, 146 [JETP Lett.JTPLA2 9, 85 (1969)].
  266. Rusinov, A. I., 1969, Zh. Eksp. Teor. Fiz.ZETFA7 56, 2047 [Sov. Phys. JETPSPHJAR 29, 1101 (1969)].
  267. Sakai, O., Y. Shimizu, H. Shiba, and K. Satori, 1993, J. Phys. Soc. Jpn.JUPSAU10.1143/JPSJ.62.3181 62, 3181.
  268. Sakurai, A., 1970, Prog. Theor. Phys.PTPKAV10.1143/PTP.44.1472 44, 1472.
  269. Salkola, M. I., A. V. Balatsky, and D. J. Scalapino, 1996, Phys. Rev. Lett.PRLTAO10.1103/PhysRevLett.77.1841 77, 1841.
  270. Salkola, M. I., A. V. Balatsky, and J. R. Schrieffer, 1997, Phys. Rev. BPRBMDO10.1103/PhysRevB.55.12648 55, 12648.
  271. Samokhin, K., and M. Walker, 2001, Phys. Rev. BPRBMDO10.1103/PhysRevB.64.024507 64, 024507.
  272. Satori, K., H. Shiba, O. Sakai, and Y. Shimizu, 1992, J. Phys. Soc. Jpn.JUPSAU10.1143/JPSJ.61.3239 61, 3239.
  273. Saxena, S. S., et al., 2000, Nature (London)NATUAS10.1038/35020500 406, 587.
  274. Scalapino, D. J., P. J. Hirschfeld, and T. Nunner, 2004, Proceedings of SNS-2004 (Sitges) (unpublished).
  275. Schachinger, E., 1982, Z. Phys. B: Condens. MatterZPCMDN10.1007/BF01318313 47, 217.
  276. Schachinger, E., and J. P. Carbotte, 1984, Phys. Rev. BPRBMDO10.1103/PhysRevB.29.165 29, 165.
  277. Schachinger, E., J. M. Daams, and J. P. Carbotte, 1980, Phys. Rev. BPRBMDO10.1103/PhysRevB.22.3194 22, 3194.
  278. Schlottmann, P., 1976, Phys. Rev. BPLRBAQ10.1103/PhysRevB.13.1 13, 1.
  279. Schmitt-Rink, S., K. Miyake, and C. M. Varma, 1986, Phys. Rev. Lett.PRLTAO10.1103/PhysRevLett.57.2575 57, 2575.
  280. Schrieffer, J. R., 1964, The Theory of Superconductivity (Benjamin, New York).
  281. Schuh, B., and E. Müller-Hartmann, 1978, Z. Phys. BZPBBDJ10.1007/BF01354836 29, 39.
  282. Segre, G. P., N. Gedik, J. Orenstein, D. A. Bonn, R. Liang, and W. N. Hardy, 2002, Phys. Rev. Lett.PRLTAO10.1103/PhysRevLett.88.137001 88, 137001.
  283. Senthil, T., and M. P. A. Fisher, 1999, Phys. Rev. BPRBMDO10.1103/PhysRevB.60.6893 60, 6893.
  284. Senthil, T., and M. P. A. Fisher, 2000, Phys. Rev. BPRBMDO10.1103/PhysRevB.61.9690 61, 9690.
  285. Senthil, T., M. P. A. Fisher, L. Balents, and C. Nayak, 1998, Phys. Rev. Lett.PRLTAO10.1103/PhysRevLett.81.4704 81, 4704.
  286. Sheehy, D. E., I. Adagideli, P. M. Goldbart, and A. Yazdani, 2001, Phys. Rev. BPRBMDO10.1103/PhysRevB.64.224518 64, 224518.
  287. Shen, Z. X., and J. R. Schrieffer, 1997, Phys. Rev. Lett.PRLTAO 78, 1991.
  288. Shiba, H., 1968, Prog. Theor. Phys.PTPKAV10.1143/PTP.40.435 40, 435.
  289. Shiba, H., 1973, Prog. Theor. Phys.PTPKAV10.1143/PTP.50.50 50, 50.
  290. Shnirman, A., I. Adagideli, P. M. Goldbart, and A. Yazdani, 1999, Phys. Rev. BPRBMDO 63, 7517.
  291. Shytov, A. V., I. Vekhter, I. A. Gruzberg, and A. V. Balatsky, 2003, Phys. Rev. Lett.PRLTAO10.1103/PhysRevLett.90.147002 90, 147002.
  292. Shytov, A. V., I. Vekhter, I. A. Gruzberg, and A. V. Balatsky, 2004, unpublished.
  293. Sidorov, V. A., M. Nicklas, P. G. Pagliuso, J. L. Sarrao, Y. Bang, A. V. Balatsky, and J. D. Thompson, 2002, Phys. Rev. Lett.PRLTAO10.1103/PhysRevLett.89.157004 89, 157004.
  294. Sigrist, M., and K. Ueda, 1991, Rev. Mod. Phys.RMPHAT10.1103/RevModPhys.63.239 63, 239.
  295. Simon, M. E., and C. M. Varma, 1999, Phys. Rev. BPRBMDO10.1103/PhysRevB.60.9744 60, 9744.
  296. Skalski, S., O. Betbeder-Matibet, and P. R. Weiss, 1964, Phys. Rev.PRVAAH10.1103/PhysRev.136.A1500 136, A1500.
  297. Soda, T., T. Matsuura, and Y. Nagaoka, 1967, Prog. Theor. Phys.PTPKAV10.1143/PTP.38.551 38, 551.
  298. Spivak, B., and S. Kivelson, 1991, Phys. Rev. BPRBMDO10.1103/PhysRevB.43.3740 43, 3740.
  299. Sprunger, P. T., L. Petersen, E. W. Plummer, E. Lægsgaard, and F. Besenbacher, 1997, ScienceSCIEAS10.1126/science.275.5307.1764 275, 1764.
  300. Stamp, P. C. E., 1987, J. Magn. Magn. Mater.JMMMDC 63-64, 429.
  301. Stipe, B., M. Rezaei, and W. Ho, 1998, ScienceSCIEAS10.1126/science.280.5370.1732 280, 1732.
  302. Suderow, H., P. Martinez-Samper, N. Luchier, J. P. Brison, S. Vieira, and P. C. Canfield, 2001, Phys. Rev. BPRBMDO10.1103/PhysRevB.64.020503 64, 020503.
  303. Takegahara, K., Y. Shimizu, and O. Sakai, 1992, J. Phys. Soc. Jpn.JUPSAU10.1143/JPSJ.61.3443 61, 3443.
  304. Takigawa, M., M. Ichioka, and K. Machida, 2003, Phys. Rev. Lett.PRLTAO10.1103/PhysRevLett.90.047001 90, 047001.
  305. Tanaka, K., and F. Marsiglio, 2000, Phys. Rev. BPRBMDO10.1103/PhysRevB.62.5345 62, 5345.
  306. Tanuma, Y., Y. Tanaka, M. Ogata, and S. Kashiwaya, 1998, J. Phys. Soc. Jpn.JUPSAU10.1143/JPSJ.67.1118 67, 1118.
  307. Timusk, T., 2003, e-print cond-mat/0303383.
  308. Timusk, T., and B. Statt, 1999, Rep. Prog. Phys.RPPHAG10.1088/0034-4885/62/1/002 62, 61.
  309. Tinkham, M., 1996, Introduction to Superconductivity, 2nd ed. (McGraw-Hill, New York).
  310. Tsai, S.-W., and P. J. Hirschfeld, 2002, Phys. Rev. Lett.PRLTAO10.1103/PhysRevLett.89.147004 89, 147004.
  311. Tsuchiura, H., Y. Tanaka, M. Ogata, and S. Kashiwaya, 2000, Phys. Rev. Lett.PRLTAO10.1103/PhysRevLett.84.3165 84, 3165.
  312. Tsuei, C. C., and J. R. Kirtley, 2000, Rev. Mod. Phys.RMPHAT10.1103/RevModPhys.72.969 72, 969.
  313. Tsuneto, T., 1962, Prog. Theor. Phys.PTPKAV10.1143/PTP.28.857 28, 857.
  314. Tu, J. J., C. C. Homes, G. D. Gu, D. N. Basov, and M. Strongin, 2002, Phys. Rev. BPRBMDO10.1103/PhysRevB.66.144514 66, 144514.
  315. Turner, P. J., et al., 2003, Phys. Rev. Lett.PRLTAO10.1103/PhysRevLett.90.237005 90, 237005.
  316. Ueda, K., and M. Rice, 1985, in Theory of Heavy Fermions and Valence Fluctuations, edited by T. Kasuya and T. Saso (Springer-Verlag, Berlin).
  317. Van Mieghem, P., 1992, Rev. Mod. Phys.RMPHAT10.1103/RevModPhys.64.755 64, 755.
  318. Varma, C. M., 1999, Phys. Rev. Lett.PRLTAO10.1103/PhysRevLett.83.3538 83, 3538.
  319. Vavilov, M. G., P. W. Brouwer, V. Ambegaokar, and C. W. J. Beenakker, 2001, Phys. Rev. Lett.PRLTAO10.1103/PhysRevLett.86.874 86, 874.
  320. Vekhter, I., A. V. Shytov, I. A. Gruzberg, and A. V. Balatsky, 2003, Physica BPHYBE3 329–333, 1446.
  321. Vekhter, I., and C. M. Varma, 2003, Phys. Rev. Lett.PRLTAO10.1103/PhysRevLett.90.237003 90, 237003.
  322. Vershinin, M., S. Misra, S. Ono, Y. Abe, Y. Ando, and A. Yazdani, 2004, ScienceSCIEAS10.1126/science.1093384 303, 1995.
  323. Vishveshwara, S., T. Senthil, and M. P. A. Fisher, 2000, Phys. Rev. BPRBMDO10.1103/PhysRevB.61.6966 61, 6966.
  324. Vojta, M., 2001, Phys. Rev. Lett.PRLTAO10.1103/PhysRevLett.87.097202 87, 097202.
  325. Vojta, M., and R. Bulla, 2001, Phys. Rev. BPRBMDO10.1103/PhysRevB.65.014511 65, 014511.
  326. Volovik, G. E., and L. P. Gor’kov, 1984, JETP Lett.JTPLA2 39, 550.
  327. Walter, H., W. Prusseit, R. Semerad, H. Kinder, W. Assmann, H. Huber, H. Burkhardt, D. Rainer, and J. A. Sauls, 1998, Phys. Rev. Lett.PRLTAO10.1103/PhysRevLett.80.3598 80, 3598.
  328. Wang, Q., and C.-R. Hu, 2004, Phys. Rev. BPRBMDO10.1103/PhysRevB.70.092505 70, 092505.
  329. Wang, Q.-H., 2002, Phys. Rev. Lett.PRLTAO10.1103/PhysRevLett.88.057002 88, 057002.
  330. Wang, Q.-H., and D.-H. Lee, 2003, Phys. Rev. BPRBMDO10.1103/PhysRevB.67.020511 67, 020511.
  331. Wang, Q.-H., and Z. D. Wang, 2004, Phys. Rev. BPRBMDO10.1103/PhysRevB.69.092502 69, 092502.
  332. Wiegmann, P. B., 1980, JETP Lett.JTPLA2 31, 367.
  333. Wilson, K. G., 1975, Rev. Mod. Phys.RMPHAT10.1103/RevModPhys.47.773 47, 773.
  334. Withoff, D., and E. Fradkin, 1990, Phys. Rev. Lett.PRLTAO10.1103/PhysRevLett.64.1835 64, 1835.
  335. Woolf, M. A., and F. Reif, 1965, Phys. Rev.PRVAAH10.1103/PhysRev.137.A557 137, A557.
  336. Wu, C., T. Xiang, and Z.-B. Su, 2000, Phys. Rev. BPRBMDO10.1103/PhysRevB.62.14427 62, 14427.
  337. Xiang, T., Y. H. Su, C. Panagopoulos, Z. B. Su, and L. Yu, 2002, Phys. Rev. BPRBMDO10.1103/PhysRevB.66.174504 66, 174504.
  338. Xiang, T., and J. M. Wheatley, 1995, Phys. Rev. BPRBMDO10.1103/PhysRevB.51.11721 51, 11721.
  339. Yafet, Y., 1963, Solid State Phys.SSPHAE10.1016/S0081-1947(08)60259-3 14, 1.
  340. Yashenkin, A. G., W. A. Atkinson, I. V. Gornyi, P. J. Hirschfeld, and D. V. Khveshchenko, 2001, Phys. Rev. Lett.PRLTAO10.1103/PhysRevLett.86.5982 86, 5982.
  341. Yazdani, A., C. M. Howald, C. P. Lutz, A. Kapitulnik, and D. M. Eigler, 1999, Phys. Rev. Lett.PRLTAO10.1103/PhysRevLett.83.176 83, 176.
  342. Yazdani, A., B. A. Jones, C. P. Lutz, M. F. Crommie, and D. M. Eigler, 1997, ScienceSCIEAS10.1126/science.275.5307.1767 275, 1767.
  343. Yoshioka, T., and Y. Ohashi, 1998, J. Phys. Soc. Jpn.JUPSAU10.1143/JPSJ.67.1332 67, 1332.
  344. Yoshioka, T., and Y. Ohashi, 2000, J. Phys. Soc. Jpn.JUPSAU10.1143/JPSJ.69.1812 69, 1812.
  345. Yu, L., 1965, Acta Phys. Sin.WLHPAR 21, 75.
  346. Zhang, D., and C. S. Ting, 2003, Phys. Rev. BPRBMDO10.1103/PhysRevB.67.100506 67, 100506.
  347. Zhang, D., and C. S. Ting, 2004, Phys. Rev. BPRBMDO10.1103/PhysRevB.69.012501 69, 012501.
  348. Zhang, G.-M., H. Hu, and L. Yu, 2001, Phys. Rev. Lett.PRLTAO10.1103/PhysRevLett.86.704 86, 704.
  349. Zhang, G.-M., H. Hu, and L. Yu, 2002, Phys. Rev. BPRBMDO10.1103/PhysRevB.66.104511 66, 104511.
  350. Zhu, J.-X., and A. Balatsky, 2002, Phys. Rev. BPRBMDO10.1103/PhysRevB.65.132502 65, 132502.
  351. Zhu, J.-X., A. V. Balatsky, T. P. Devereaux, Q. Si, J. Lee, K. McElroy, and J. C. Davis, 2005, e-print cond-mat/0507610.
  352. Zhu, J.-X., W. Kim, C. S. Ting, and J. P. Carbotte, 2001, Phys. Rev. Lett.PRLTAO10.1103/PhysRevLett.87.197001 87, 197001.
  353. Zhu, J.-X., T. K. Lee, C. R. Hu, and C. S. Ting, 2000, Phys. Rev. BPRBMDO10.1103/PhysRevB.61.8667 61, 8667.
  354. Zhu, J.-X., I. Martin, and A. R. Bishop, 2002, Phys. Rev. Lett.PRLTAO10.1103/PhysRevLett.89.067003 89, 067003.
  355. Zhu, J.-X., K. McElroy, J. Lee, T. P. Devereaux, Q. Si, J. C. Davis, and A. V. Balatsky, 2005, e-print cond-mat/0507621.
  356. Zhu, J.-X., D. N. Sheng, and C. S. Ting, 2000, Phys. Rev. Lett.PRLTAO10.1103/PhysRevLett.85.4944 85, 4944.
  357. Zhu, J.-X., J. Sun, Q. Si, and A. V. Balatsky, 2004, Phys. Rev. Lett.PRLTAO10.1103/PhysRevLett.92.017002 92, 017002.
  358. Zhu, J.-X., and C. S. Ting, 2001a, Phys. Rev. BPRBMDO 63, 020506.
  359. Zhu, J.-X., and C. S. Ting, 2001b, Phys. Rev. BPRBMDO 64, 060501.
  360. Zhu, J.-X., and C. S. Ting, 2001c, Phys. Rev. Lett.PRLTAO 87, 147002.
  361. Zhu, J.-X., C. S. Ting, and C. R. Hu, 2000, Phys. Rev. BPRBMDO10.1103/PhysRevB.62.6027 62, 6027.
  362. Zhu, L., W. A. Atkinson, and P. J. Hirschfeld, 2003, Phys. Rev. BPRBMDO10.1103/PhysRevB.67.094508 67, 094508.
  363. Zhu, L., W. A. Atkinson, and P. J. Hirschfeld, 2004, Phys. Rev. BPRBMDO10.1103/PhysRevB.69.060503 69, 060503.
  364. Zhu, L., P. J. Hirschfeld, and D. J. Scalapino, 2004, Phys. Rev. BPRBMDO10.1103/PhysRevB.70.214503 70, 214503.
  365. Ziegler, K., 1996, Phys. Rev. BPRBMDO10.1103/PhysRevB.53.9653 53, 9653.
  366. Ziegler, K., M. H. Hettler, and P. J. Hirschfeld, 1996, Phys. Rev. Lett.PRLTAO10.1103/PhysRevLett.77.3013 77, 3013.
  367. Zittartz, J., A. Bringer, and E. Müller-Hartmann, 1972, Solid State Commun.SSCOA410.1016/0038-1098(72)90056-7 10, 513.
  368. Zittartz, J., and J. S. Langer, 1966, Phys. Rev.PHRVAO10.1103/PhysRev.148.741 148, 741.
  369. Zittartz, J., and E. Müller-Hartmann, 1970, Z. Phys.ZEPYAA10.1007/BF01394943 232, 11.

Outline

Information

Rev. Mod. Phys. 78, 373– Published 9 May, 2006

    © 2006 American Physical Society

    Sign In to Your Journals Account

    Filter

    Filter

    Article Lookup

    Enter a citation