Quantum impurity dynamics in two-dimensional antiferromagnets and superconductors

Physical Review B - Condensed Matter and Materials Physics

Volumn 61, Issue 22, 2000, Pages 15152-15184

  Vojta, Matthias ^a   Buragohain, Chiranjeeb ^a   Sachdev, Subir ^a  

^a Yale University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000684993     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.61.15152     Document Type: Article

References (113)

1. M. Hase, I. Terasaki, Y. Sasago, K. Uchinokura, and H. Obara, Phys. Rev. Lett. 71, 4059 (1993).
2. S. B. Oseroff, S.-W. Cheong, B. Aktas, M. F. Hundley, Z. Fisk, and L. W. Rupp, Jr., Phys. Rev. Lett. 74, 1450 (1995).
3. K. M. Kojima et. al Phys. Rev. Lett. 79, 503 (1997).
4. T. Masuda, A. Fujioka, Y. Uchiyama, I. Tsukada, and K. Uchinokura, Phys. Rev. Lett. 80, 4566 (1998).
5. Y. Uchiyama, Y. Sasago, I. Tsukada, K. Uchinokura, A. Zheludev, T. Hayashi, N. Miura, and P. Böni, Phys. Rev. Lett. 83, 632 (1999).
6. A. M. Finkelstein, V. E. Kataev, E. F. Kukovitskii, and G. B. Teitel’baum, Physica C 168, 370 (1990).
7. H. Alloul, P. Mendels, H. Casalta, J. F. Marucco, and J. Arabski, Phys. Rev. Lett. 67, 3140 (1991).
8. A. V. Mahajan, H. Alloul, G. Collin, and J. F. Marucco, Phys. Rev. Lett. 72, 3100 (1994).
9. B. Nachumi et. al Phys. Rev. Lett. 77, 5421 (1996).
10. J. Bobroff et. al Phys. Rev. Lett. 79, 2117 (1997).
11. D. L. Sisson, S. G. Doettinger, A. Kapitulnik, R. Liang, D. A. Bonn, and W. N. Hardy, Phys. Rev. B 61, 3604 (2000).
12. P. Mendels, J. Bobroff, G. Collin, H. Alloul, M. Gabay, J. F. Marucco, N. Blanchard, and B. Grenier, Europhys. Lett. 46, 678 (1999).
13. J. Bobroff, W. A. MacFarlane, H. Alloul, P. Mendels, N. Blanchard, G. Collin, and J.-F. Marucco, Phys. Rev. Lett. 83, 4381 (1999).
14. M.-H. Julien, T. Feher, M. Horvatic, C. Berthier, O. N. Bakharev, P. Segransan, G. Collin, and J.-F. Marucco, Phys. Rev. Lett. 84, 3422 (2000).
15. 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. Lett. 82, 1939 (1999).
16. S. H. Pan, E. W. Hudson, K. M. Lang, H. Eisaki, S. Uchida, and J. C. Davis, Nature (London) 403, 746 (2000).
17. J. Rossat-Mignod, L. P. Regnault, C. Vettier, P. Bourges, P. Burlet, J. Bossy, J. Y. Henry, and G. Lapertot, Physica C 185-189, 86 (1991).
18. H. A. Mook, M. Yehiraj, G. Aeppli, T. E. Mason, and T. Armstrong, Phys. Rev. Lett. 70, 3490 (1993).
19. H. F. Fong, B. Keimer, F. Dogan, and I. A. Aksay, Phys. Rev. Lett. 78, 713 (1997).
20. P. Bourges, in The Gap Symmetry and Fluctuations in High Temperature Superconductors, edited by J. Bok, G. Deutscher, D. Pavuna, and S. A. Wolf (Plenum, New York, 1998).
21. H. He, Y. Sidis, P. Bourges, G. D. Gu, A. Ivanov, N. Koshizuka, B. Liang, C. T. Lin, L. P. Regnault, E. Schoenherr, and B. Keimer, cond-mat/0002013 (unpublished).
22. C. C. Wan, A. B. Harris, and D. Kumar, Phys. Rev. B 48, 1036 (1993).
23. N. Bulut, cond-mat/9908266 (unpublished).
24. N. Bulutcond-mat/9909437 (unpublished).
25. S. Sachdev, C. Buragohain, and M. Vojta, Science 286, 2479 (1999).
26. S. Sachdev, Quantum Phase Transitions (Cambridge University Press, Cambridge, England, 1999).
27. see also S. Sachdev, Phys. World 12 (4), 33 (1999).
28. N. Read and S. Sachdev, Phys. Rev. Lett. 62, 1694 (1989).
29. N. ReadS. SachdevPhys. Rev. B 42, 4568 (1990).
30. A. V. Chubukov, S. Sachdev, and J. Ye, Phys. Rev. B 49, 11 919 (1994).
31. N. Katoh and M. Imada, J. Phys. Soc. Jpn. 63, 4529 (1994).
32. M. Imada and Y. Iino, J. Phys. Soc. Jpn. 66, 568 (1997).
33. V. N. Kotov, O. P. Sushkov, Zheng Weihong, and J. Oitmaa, Phys. Rev. Lett. 80, 5790 (1998).
34. J. Tworzydlo, O. Y. Osman, C. N. A. van Duin, and J. Zaanen, Phys. Rev. B 59, 115 (1999).
35. V. N. Kotov, J. Oitmaa, and Zheng Weihong, Phys. Rev. B 59, 11 377 (1999).
36. S. Sachdev and M. Vojta, cond-mat/9908008 (unpublished).
37. T. Matsuda and K. Hida, J. Phys. Soc. Jpn. 59, 2223 (1990).
38. J. Phys. Soc. Jpn.K. Hida, 59, 2230 (1990).
39. J. Phys. Soc. Jpn.K. Hida67, 1540 (1998).
40. A. J. Millis and H. Monien, Phys. Rev. Lett. 70, 2810 (1993).
41. A. W. Sandvik and D. J. Scalapino, Phys. Rev. Lett. 72, 2777 (1994).
42. A. W. Sandvik, A. V. Chubukov, and S. Sachdev, Phys. Rev. B 51, 16 483 (1995).
43. M. P. Gelfand, Phys. Rev. B 53, 11 309 (1996).
44. Y. Matsushita, M. P. Gelfand, and C. Ishii, J. Phys. Soc. Jpn. 66, 3648 (1997).
45. M. P. Gelfand, Zheng Weihong, C. J. Hamer, and J. Oitmaa, Phys. Rev. B 57, 392 (1998).
46. M. Troyer and S. Sachdev, Phys. Rev. Lett. 81, 5418 (1998).
47. M. Troyer, M. Imada, and K. Ueda, J. Phys. Soc. Jpn. 66, 2957 (1997).
48. N. Read and S. Sachdev, Phys. Rev. Lett. 66, 1773 (1991).
49. S. Sachdev and N. Read, Int. J. Mod. Phys. B 5, 219 (1991).
50. V. N. Kotov, J. Oitmaa, O. P. Sushkov, and Zheng Weihong, Phys. Rev. B 60, 14 613 (1999).
51. R. R. P. Singh, Zheng Weihong, C. J. Hamer, and J. Oitmaa, Phys. Rev. B 60, 7278 (1999).
52. V. N. Kotov and O. P. Sushkov, cond-mat/9907178 (unpublished).
53. S. Sachdev and J. Ye, Phys. Rev. Lett. 69, 2411 (1992).
54. N. Nagaosa, A. Furusaki, M. Sigrist, and H. Fukuyama, J. Phys. Soc. Jpn. 65, 3724 (1996).
55. S. Sachdev and J. Ye, Phys. Rev. Lett. 70, 3339 (1993).
56. A. Georges, O. Parcollet, and S. Sachdev, cond-mat/9909239 (unpublished).
57. J. L. Smith and Q. Si, cond-mat/9705140 (unpublished).
58. J. L. SmithQ. SiEurophys. Lett. 45, 228 (1999).
59. A. M. Sengupta, Phys. Rev. B 61, 4041 (2000).
60. J. L. Cardy, Scaling and Renormalization in Statistical Physics (Cambridge University Press, Cambridge, England, 1996), Chap. 7.
61. Y. C. Chen and A. H. Castro Neto, Phys. Rev. B 61, R3772 (2000).
62. D. C. Mattis, Phys. Lett. 56A, 421 (1976).
63. D. L. Liu, Y. Zha, and K. Levin, Phys. Rev. Lett. 75, 4130 (1995).
64. D. K. Morr and D. Pines, Phys. Rev. Lett. 81, 1086 (1998).
65. J. Brinckmann and P. A. Lee, Phys. Rev. Lett. 82, 2915 (1999).
66. S.-C. Zhang, Science 275, 1089 (1997).
67. L. Balents, M. P. A. Fisher, and C. Nayak, Int. J. Mod. Phys. B 12, 1033 (1998).
68. P. A. Lee, Phys. Rev. Lett. 71, 1887 (1993).
69. A. V. Balatsky, M. I. Salkola, and A. Rosengren, Phys. Rev. B 51, 15 547 (1995).
70. M. I. Salkola, A. V. Balatsky, and D. J. Scalapino, Phys. Rev. Lett. 77, 3909 (1996).
71. M. Franz, C. Kallin, and A. J. Berlinsky, Phys. Rev. B 54, 6897 (1996).
72. C. R. Cassanello and E. Fradkin, Phys. Rev. B 56, 11 246 (1997).
73. N. Nagaosa and P. A. Lee, Phys. Rev. Lett. 79, 3755 (1997).
74. H. Tanaka, K. Kuboki, and M. Sigrist, Int. J. Mod. Phys. B 12, 2447 (1998).
75. H. Tsuchiura, Y. Tanaka, M. Ogata, and S. Kashiwaya, cond-mat/9906022 (unpublished).
76. H. TsuchiuraY. TanakaM. OgataS. Kashiwayacond-mat/9911117 (unpublished).
77. R. Kilian, S. Krivenko, G. Khaliullin, and P. Fulde, Phys. Rev. B 59, 14 432 (1999).
78. C. Pépin and P. A. Lee, Phys. Rev. Lett. 81, 2779 (1998).
79. C. PépinP. A. Leecond-mat/0002227(unpublished). These papers consider d-wave superconductors with purely potential scattering and no independent spin degrees of freedom on the impurities; however, they succeeded in obtaining nonperturbative results for a finite density of impurities. They show that in the unitarity limit of potential scattering, quasibound states form at the impurity sites at the Fermi level. We believe that after accounting for the strong local Coulomb repulsion (neglected by Pépin and Lee), each bound state will capture only a single electron, and the low energy physics will then be described by impurity spin models similar to those considered in our paper; the residual impurity potential scattering in the resulting models will not be in the unitarity limit.
80. D. Withoff and E. Fradkin, Phys. Rev. Lett. 64, 1835 (1990).
81. K. Chen and C. Jayaprakash, J. Phys.: Condens. Matter 7, L491 (1995).
82. K. Ingersent, Phys. Rev. B 54, 11 936 (1996).
83. Phys. Rev. BC. Gonzalez-Buxton and K. Ingersent, 57, 14 254 (1998).
84. R. Bulla, Th. Pruschke, and A. C. Hewson, J. Phys.: Condens. Matter 9, 10 463 (1997).
85. K. Ingersent and Q. Si, cond-mat/9810226 (unpublished).
86. A. V. Chubukov and S. Sachdev, Phys. Rev. Lett. 71, 169 (1993).
87. P. Nozières and A. Blandin, J. Phys. (Paris) 41, 193 (1980).
88. V. Barzykin and I. Affleck, Phys. Rev. B 57, 432 (1998).
89. I. Affleck and A. W. W. Ludwig, Nucl. Phys. B 352, 849 (1991).
90. Nucl. Phys. BI. AffleckA. W. W. Ludwig360, 641 (1991).
91. I. AffleckA. W. W. LudwigPhys. Rev. Lett. 67, 161 (1991).
92. O. Parcollet and A. Georges, Phys. Rev. Lett. 79, 4665 (1997).
93. O. Parcollet, A. Georges, G. Kotliar, and A. M. Sengupta, Phys. Rev. B 58, 3794 (1998).
94. E. Brézin, J. C. Le Guillou, and J. Zinn-Justin, in Phase Transitions and Critical Phenomena, edited by C. Domb and M. S. Green (Academic, London, 1976), Vol. 6.
95. A. C. Hewson, The Kondo Problem to Heavy Fermions (Cambridge University Press, Cambridge, England, 1997).
96. S. Sachdev, Phys. Rev. B 55, 142 (1997).
97. S. Sachdev, Z. Phys. B: Condens. Matter 94, 469 (1994).
98. F. J. Dyson, Phys. Rev. 102, 1230 (1956).
99. S. Maleev, Zh. Eksp. Teor. Fiz. 33, 1010 (1957) [Sov. Phys. JETP 6, 776 (1958)].
100. A. I. Akhiezer, V. G. Bar’yakhtar, and S. V. Peletminskii, Spin Waves (North-Holland, Amsterdam, 1968), Chap. 8.
101. A. W. Sandvik, E. Dagotto, and D. J. Scalapino, Phys. Rev. B 56, 11 701 (1997).
102. S. Das Sarma, S. Sachdev, and L. Zheng, Phys. Rev. B 58, 4672 (1998).
103. N. E. Bickers, Rev. Mod. Phys. 59, 845 (1987).
104. D. L. Cox and A. E. Ruckenstein, Phys. Rev. Lett. 71, 1613 (1993).
105. S. Sachdev and R. N. Bhatt, Phys. Rev. B 41, 9323 (1990).
106. S. Gopalan, T. M. Rice, and M. Sigrist, Phys. Rev. B 49, 8901 (1994).
107. A. M. Tsvelik, Quantum Field Theory in Condensed Matter Physics (Cambridge University Press, Cambridge, England, 1995).
108. Ar. Abanov and A. V. Chubukov, Phys. Rev. Lett. 83, 1652 (1999).
109. M. R. Norman and H. Ding, Phys. Rev. B 57, R11 089 (1998).
110. 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).
111. A. V. Chubukov, N. Gemelke, and Ar. Abanov, cond-mat/9910090 (unpublished).
112. M. Abramowitz and I. Stegun, Handbook of Mathematical Functions (Dover, New York, 1965).
113. O. Zachar, S. A. Kivelson, and V. J. Emery, Phys. Rev. B 57, 1422 (1998).