Duality in Josephson junction arrays

Nuclear Physics B - Proceedings Supplements

Volumn 58, Issue 1-3, 1997, Pages 79-90

  Blanter, Ya M ^a   Fazio, Rosario ^b   Schön, Gerd ^c  

^a UNIVERSITY OF GENEVA   (Switzerland)

^b UNIVERSITY OF CATANIA   (Italy)

^c UNIVERSITY OF KARLSRUHE   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031231923     PISSN: 09205632     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0920-5632(97)00414-3     Document Type: Article

References (53)

1. 1. H. A. Kramers and G. H. Wannier, Phys. Rev. 60, 252 (1941).
2. 2. R. Savit, Rev. Mod. Phys. 52, 453 (1980).
3. 3. J. V. José, L. P. Kadanoff, S. Kirkpatrick, and D. R. Nelson, Phys. Rev. B 16, 1217 (1977).
4. 4. L. P. Kadanoff, J. Phys. A 11, 1399 (1978).
5. 5. B. Nienhuis, in: Phase transitions and critical phenomena, Vol. 11, ed. by C. Domb and J. L. Lebowitz (Academic Press, London, 1987), p.1.
6. 6. see e.g. Proceedings of the NATO ARW Coherence in Superconducting Networks, J.E. Mooij and G. Schön eds., Physica B152, (1988); J.E. Mooij and G. Schön, in: Single Charge Tunneling, H. Grabert and M. H. Devoret eds. (Plenum, N. Y., 1992).
7. 6. see e.g. Proceedings of the NATO ARW Coherence in Superconducting Networks, J.E. Mooij and G. Schön eds., Physica B152, (1988); J.E. Mooij and G. Schön, in: Single Charge Tunneling, H. Grabert and M. H. Devoret eds. (Plenum, N. Y., 1992).
8. 7. J. M. Kosterlitz and D. J. Thouless, J. Phys. C 6, 1181 (1973).
9. 8. B. I. Halperin and D. R. Nelson, J. Low. Temp. Phys. 36, 599 (1979).
10. 9. V. L. Berezinskii, Zh. Eksp. Theor. Fiz. 59, 907 (1970) [Sov. Phys. - JETP 32, 493 (1971)].
11. 9. V. L. Berezinskii, Zh. Eksp. Theor. Fiz. 59, 907 (1970) [Sov. Phys. - JETP 32, 493 (1971)].
12. 10. E. H. Hauge and P. C. Hemmer, Phys. Norvegica 5, 209 (1971).
13. 11. J. M. Kosterlitz, J. Phys. C 7, 1046 (1974).
14. 12. P. Minnhagen, Rev. Mod. Phys. 59, 1001 (1987).
15. 13. G. Schön and A. D. Zaikin, Phys. Reports 198, 237 (1990).
16. 14. R. Fazio and G. Schön, Phys. Rev. B 43, 5307 (1991).
17. 15. F. Guinea and G. Schön, J. Low. Temp. Phys. 69, 219 (1987); G. Schön and A. D. Zaikin, Physica B 152, 203 (1988); S. M. Apenko, Phys. Lett. A 142, 277 (1989).
18. 15. F. Guinea and G. Schön, J. Low. Temp. Phys. 69, 219 (1987); G. Schön and A. D. Zaikin, Physica B 152, 203 (1988); S. M. Apenko, Phys. Lett. A 142, 277 (1989).
19. 15. F. Guinea and G. Schön, J. Low. Temp. Phys. 69, 219 (1987); G. Schön and A. D. Zaikin, Physica B 152, 203 (1988); S. M. Apenko, Phys. Lett. A 142, 277 (1989).
20. 16. B. Abeles, Phys. Rev. B 15, 2828 (1977).
21. 17. K. B. Efetov, Zh. Eksp. Theor. Fiz. 78, 2017 (1980) [Sov. Phys. - JETP 51, 1015 (1980)].
22. 17. K. B. Efetov, Zh. Eksp. Theor. Fiz. 78, 2017 (1980) [Sov. Phys. - JETP 51, 1015 (1980)].
23. 18. E. Šimánek, Phys. Rev. Lett. 45, 1442 (1980).
24. 19. S. Doniach, Phys. Rev. B 24, 5063 (1981).
25. 20. Yu. E. Lozovik and S. G. Akopov, J. Phys. C 14, L31 (1981).
26. 21. L. J. Jacobs, J. V. José and M. A. Novotny, Phys. Rev. Lett. 53, 2177 (1984).
27. 22. R. S. Fishman and D. Stroud, Phys. Rev. B 38, 290 (1988).
28. 23. J. V. José, Phys. Rev. B 29, 2836 (1984); see also J. V. José and C. Rojas, Physica B 203, 481 (1994).
29. 23. J. V. José, Phys. Rev. B 29, 2836 (1984); see also J. V. José and C. Rojas, Physica B 203, 481 (1994).
30. 24. M. .C. Diamantini, P. Sodano and C. A. Trugenberger Phys. Rev. Lett. 75, 3517 (1995).
31. 25. M. P. A. Fisher, G. Grinstein, and S. M. Girvin, Phys. Rev. Lett. 64, 587 (1990).
32. 26. J. E. Mooij, B. J. van Wees, L. J. Geerligs, M. Peters, R. Fazio, and G. Schön, Phys. Rev. Lett. 65, 645 (1990).
33. 27. R. Fazio, U. Geigenmüller, and G. Schön, in Quantum Fluctuations in Mesoscopic and Macroscopic Systems, H. A. Cerdeira, et al. eds. (World Scientific, 1991), p. 214.
34. 28. See the appendix of: D. R. Nelson and B. I. Halperin, Phys. Rev. B 21, 5312 (1980).
35. n = ±1.
36. 30. E. Šimánek, Sol. State. Commun. 48, 1023 (1983).
37. 31. U. Eckern and A. Schmid, Phys. Rev. B 39, 6441 (1989).
38. 32. In 1D Josephson chains, in the presence of extra inductive terms charge solitons with a larger mass may appear as topological excitations. See Z. Hermon, E. Ben-Jacob, and G. Schön, Phys. Rev. B 54, 1234 (1996).
39. 33. This situation is quite different from multi-layered systems with Josephson coupling between layers, that have been discussed in the literature: see e.g. S. R. Shenoy, Phys. Rev. B 42, 8595 (1990); N. K. Kultanov and Yu. E. Lozovik, Sol. St. Commun. 88, 645 (1993). The analog of the BKT transition in these systems is the disruption of vortex rings. In the limit of weak Josephson coupling this system is reduced to the 2D XY-model, while in the opposite case of strong coupling it is essentially the 3D XY-model.
40. 33. This situation is quite different from multi-layered systems with Josephson coupling between layers, that have been discussed in the literature: see e.g. S. R. Shenoy, Phys. Rev. B 42, 8595 (1990); N. K. Kultanov and Yu. E. Lozovik, Sol. St. Commun. 88, 645 (1993). The analog of the BKT transition in these systems is the disruption of vortex rings. In the limit of weak Josephson coupling this system is reduced to the 2D XY-model, while in the opposite case of strong coupling it is essentially the 3D XY-model.
41. 34. Ya. M. Blanter and G. Schön, Phys. Rev. B 53, 14534 (1996).
42. 35. C. Rojas, J. V. José, and A. M. Tikofsky, Bull. Am. Phys. Soc. 40, p.68, B11-7 (1995); J. V. José, private communication.
43. 35. C. Rojas, J. V. José, and A. M. Tikofsky, Bull. Am. Phys. Soc. 40, p.68, B11-7 (1995); J. V. José, private communication.
44. 36. R. Fazio, A. van Otterlo, G. Schön, H. S. J. van der Zant, and J. E. Mooij, Helv. Physica Acta 65, 228 (1992).
45. 37. F. Gaitan and S. R. Shenoy, Phys. Rev. Lett. 76, 4404 (1996).
46. 38. X.-M. Zhu, Y. Tan, and P. Ao, cond-mat/9507126.
47. 39. Yu. G. Makhlin and G. E. Volovik, Pis'ma Zh. Eksp. Teor. Fiz. 62, 923 (1985) [JETP Lett. 62, 941 (1995)].
48. 39. Yu. G. Makhlin and G. E. Volovik, Pis'ma Zh. Eksp. Teor. Fiz. 62, 923 (1985) [JETP Lett. 62, 941 (1995)].
49. 40. E. B. Sonin, cond-mat/9606099; Phys. Rev. B, to be published.
50. 41. A. van Otterlo, G. Schön, and G. Blatter, Comment submitted to Phys. Rev. Lett.
51. 42. J. Villain, J.Physique 36, 581 (1975).
52. 43. A. van Otterlo, K.-H. Wagenblast, R. Baltin, C. Bruder, R. Fazio, and G. Schön, Phys. Rev. B 52, 16176 (1995).
53. 44. S. Elitzur, R. Pearson, and J. Shigemitzu, Phys. Rev. D 19, 3638 (1979).