Persistent currents, flux quantization and magnetomotive forces in normal metals and superconductors (Review Article)

Физика Низких Температур: Том 36, Выпуск 10-11 (Октябрь 2010), c. 1057-1065 ( к оглавлению , назад )

Persistent currents, flux quantization and magnetomotive forces in normal metals and superconductors (Review Article)

Igor O. Kulik

Department of Physics and Astronomy, State University of New York at Stony Brook SUNY Stony Brook, NY 11794-3800, USA
E-mail: i.o.kulik@gmail.com

Received May 12, 2010

Abstract

The notion of persistent current comes back to orbital currents in normal metals, semiconductors and even insulators displaying diamagnetic behavior in weak magnetic fields, but came to focus at the discovery of current persistence and magnetic flux quantization at large fields in atomically big but macroscopically small (mesoscopic) objects. The phenomenon bears much similarity with supercurrents in superconductive metals. We will review progress in developing of our understanding of the physical and technological aspects of this phenomenon. The exact solution for currents, magnetic moments and magnetomotive forces (torques) in crossed magnetic fields are presented. Time-dependent phenomena in crossed magnetic and electric fields, and in possibility of spontaneous persistent currents and of work extraction from static and dynamic quantum states are discussed.

PACS: 73.23.–b Electronic transport in mesoscopic systems;
PACS: 03.65.Ta Foundations of quantum mechanics; measurement theory;
PACS: 71.10.pm Fermions in reduced dimensions (anyons, composite fermions, Luttinger liquid, etc.).

Key words: Aharonov–Bohm effect, Berry phase, qubit, Coulomb blocade, Luttinger liquid.

References

1. Diamagnetism and Paramagnetism, in: C. Kittel, Introduction to Solid State Physics, 7th edition, Ch. 14. J. Willey, New York (1996). Google Scholar

2. F. London, Superfluids, Vol. 1., Dover Publ., New York (1961). Google Scholar

3. L. D. Landau, Zs. Phys. 64, 629 (1930). CrossRef Google Scholar

4. E. Teller, Zs. Phys. 67, 311 (1931). CrossRef Google Scholar

5. R. E. Peierls, Quantum Theory of Solids, Clarendon Press, Oxford (1955). Google Scholar

6. I. M. Lifshitz, M. Ya. Azbel, and M. I. Kaganov,Nauka Publ., Moscow (1971). Google Scholar

7. J. M. Ziman, Principles of the Theory of Solids, University Press, Cambridge (1964). Google Scholar

8. D. Shoenberg, Magnetic Oscillations in Metals, Cambridge University Press (1984). Google Scholar

9. J. H. van Leeuwen, J. Phys. (Paris), Colloq. 2, 361 (1921). Google Scholar

10. K. Richter, D. Ullmo, and R. A. Jalabert, Phys. Rep. 276, 1 (1996). CrossRef Google Scholar

11. E. Gurevich and S. Shapiro, J. Phys. I 7, 807 (1997). CrossRef Google Scholar

12. S. S. Nedorezov, Zh. Eksp. Teor. Fiz. 64, 624 (1973) S. S. Nedorezov[Sov. Phys. JETP 37, 317 (1973)].CAS Google Scholar

13. I. O. Kulik, in I. O. Kulik and R. Ellialtioglu (eds.), Quantum Mesoscopic Phenomena in Microelectronics, Ch. 7, p. 260, Kluwer Academic Publ., Dordrecht (2000). Google Scholar

14. B. I. Halperin, Phys. Rev. B 25, 2185 (1982). CrossRef Google Scholar

15. Y. Aharonov and D. Bohm, Phys. Rev. 115, 485 (1961); CrossRef Google Scholar

16. F. Hund, Calculation Concerning the Magnetic Behavior of Small Metallic Particles at Low Temperatures [reprinted from Ann. Phys. 32, 102 (1938)] CrossRef Google Scholar

17. H. Froelich, Proc. R. Soc. London, Ser. A 223, 296 (1954). CrossRef Google Scholar

18. N. Byers and C. N. Yang, Phys. Rev. Lett. 7, 2 (1961); CrossRef Google Scholar

19. J. M. Blatt, Theory of Superconductivity, Academic Press, New York (1964). Google Scholar

20. M. Schick, Phys. Rev. 166, 404 (1968). CrossRef Google Scholar

21. L. Gunther and Y. Imry, Solid State Commun. 7, 1391 (1969). CrossRef Google Scholar

22. F. Bloch, Phys. Rev. B 2, 109 (1970); CrossRef Google Scholar

23. R. B. Dingle, Proc. R. Soc. London, Ser. A 212, 47 (1952); CrossRef Google Scholar

24. I. O. Kulik, Pis'ma Zh. Eksp. Teor. Fiz. 11, 407 (1970) I. O. Kulik,[JETP Lett. 11, 275 (1970)]; I. O. Kulik,Zh. Eksp. Teor. Fiz. 58, 217 (1970) I. O. Kulik,[Sov. Phys. JETP 31, 1172 (1970)].CAS Google Scholar

25. M. Buttiker, Y. Imry, and R. Landauer, Phys. Lett. A96, 365 (1983). Google Scholar

26. B. L. Altshuler, A. G. Aronov, and B. Z. Spivak, Pis'ma Zh. Eksp. Teor. Fiz. 33, 101 (1981) B. L. Altshuler, A. G. Aronov, and B. Z. Spivak,[JETP Lett. 33, 94 (1981)] B. L. Altshuler, A. G. Aronov, and B. Z. Spivak,[JETP Lett. 33, 94 (1981)]. Google Scholar

27. A. G. Aronov and Yu. V. Sharvin, Rev. Mod. Phys. 59, 755 (1987). CrossRef Google Scholar

28. D. Yu. Sharvin, and Yu. V. Sharvin, Pis'ma Zh. Eksp. Teor. Fiz. 34, 285 (1981) D. Yu. Sharvin, and Yu. V. Sharvin,[JETP Lett. 34, 272 (1981)].CAS Google Scholar

29. A. A. Shablo, T. P. Narbut, S. A. Tyurin, and I. M. Dmitrenko, JETP Lett. 19, 246 (1974). Google Scholar

30. V. Ambegaokar and U. Eckern, Phys. Rev. Lett. 65, 381 (1990). CrossRef Google Scholar

31. E. N. Bogachek and G. A. Gogadze, Zh. Eksp. Teor. Fiz. 63, 1839 (1972) E. N. Bogachek and G. A. Gogadze,[Sov. Phys. JETP 36, 973 (1973)]. Google Scholar

32. J. B. Keller and S. I. Rubinov, Ann. Phys. 9, 24 (1960). CrossRef Google Scholar

33. N. B. Brandt, D. V. Gitsu, A. A. Nikolaeva, and Ya. G. Ponomarev, Pis'ma Zh. Eksp. Teor. Fiz. 24, 304 (1976) N. B. Brandt, D. V. Gitsu, A. A. Nikolaeva, and Ya. G. Ponomarev[JETP Lett. 24, 272 (1976)]; CrossRef Google Scholar

34. E. N. Bogachek and G. A. Gogadze, Zh. Eksp. Teor. Fiz. Pis'ma Red. 17, 164 (1973). Google Scholar

35. E. N. Bogachek and U. Landman, Phys. Rev. B 52, 14067 (1995). CrossRef Google Scholar

36. O. Costa de Beauregard and J. M. Vigoureux, Phys. Rev. D 9, 1626 (1974); CrossRef Google Scholar

37. E. N. Bogachek and G. A. Gogadze, Zh. Eksp. Teor. Fiz. 67, 621 (1994). Google Scholar

38. R. Landauer and M. Buttiker, Phys. Rev. Lett. 54, 2049 (1985). CrossRef Google Scholar

39. Y. Imry and N. S. Shiren, Phys. Rev. B 33, 7992 (1986). CrossRef Google Scholar

40. A. M. Zagoskin and I. O. Kulik, Fiz. Nizk. Temp. 16, 911 (1990) A. M. Zagoskin and I. O. Kulik,[Sov. J. Low Temp. Phys. 16, 533 (1990)]. Google Scholar

41. E. N. Bogachek, A. M. Zagoskin, and I. O. Kulik, Fiz. Nizk. Temp. 16, 1404 (1990) E. N. Bogachek, A. M. Zagoskin, and I. O. Kulik[Sov. J. Low Temp. Phys. 16, 796 (1990)]. Google Scholar

42. I. O. Kulik, Nonlinear Phenomena in Metallic Contacts, in: Quantum Mesoscopic Phenomena and Mesoscopic Devices in Microelectronics, Ch. 1, p. 3, I. O. Kulik and R. Ellialtioglu (eds.), Kluwer Academic Publ., Dordrecht (2000). Google Scholar

43. M. Ya. Azbel', Phys. Rev. B 48, 4592 (1993). CrossRef Google Scholar

44. I. V. Krive and A. Naftulin, Nucl. Phys. B364, 541 (1991). CrossRef Google Scholar

45. E. N. Bogachek, I. V. Krive, I. O. Kulik, and A. S. Rozhavsky, Phys. Rev. B 42, 7614 (1990). CrossRef Google Scholar

46. E. N. Bogachek, I. V. Krive, I. O. Kulik, and A. S. Rozhavsky, Zh. Eksp. Teor. Fiz. 97, 603 (1990). Google Scholar

47. A. S. Rozhavsky, Fiz. Nizk. Temp. 22, 462 (1996) A. S. Rozhavsky,[Low Temp. Phys. 22, 322 (1996)]. Google Scholar

48. I. O. Kulik, A. S. Rozhavskii, and E. N. Bogachek, Pis'ma Zh. Eksp. Teor. Fiz. 47, 251 (1988). Google Scholar

49. W. P. Su, J. R. Schrieffer, and A. J. Heeger, Phys. Rev. Lett. 42, 1698 (1979). CrossRef Google Scholar

50. G. Montambaux, Eur. Phys. J. B 1, 377 (1998). CrossRef Google Scholar

51. T. Matsuura, T. Tsuneta, K. Inagaki, and S. Tanda, Phys. Rev. B 73, 165118 (2006). CrossRef Google Scholar

52. Shi-Dong Liang, Yi-Hong Bai, and Bo Beng, Phys. Rev. B 74, 113304 (2006). CrossRef Google Scholar

53. I. V. Krive and A. S. Rozhavsky, Int. J. Mod. Phys. B 6, 1255 (1992). CrossRef Google Scholar

54. Yu. I. Latyshev, O. Laborde, P. Monceau, and S. Klaumunzer, Phys. Rev. Lett. 78, 919 (1997). CrossRef Google Scholar

55. E. P. Wigner, Phys. Rev. 46, 1002 (1934). CrossRef Google Scholar

56. I. O. Kulik and R. I. Shekhter, Zh. Eksp. Teor. Fiz. 68, 623 (1975) I. O. Kulik and R. I. Shekhter,[Sov. Phys. JETP 41, 308 (1975)]. Google Scholar

57. D. V. Averin and K. K. Likharev, in Mesoscopic Phenomena in Solids, B. L. Altshuler, P. A. Lee, and R. A. Webb (eds.), Elsevier, Amsterdam (1991). Google Scholar

58. S. Tomonaga, Prog. Theor. Phys. 5, 544 (1950); CrossRef Google Scholar

59. L. I. Glazman, I. M. Ruzin, and B. I. Shklovskii, Phys. Rev. B 45, 8454 (1992). CrossRef Google Scholar

60. D. L. Maslov, M. Stone, P. M. Goldbart, and D. Loss, Phys. Rev. B 53, 1548 (1996). CrossRef Google Scholar

61. P. Sandstrom and I. V. Krive, Ann. Phys. 257, 18 (1997). CrossRef Google Scholar

62. M. V. Moskalets, Photonics Spectra 4, 17 (1999). Google Scholar

63. M. V. Moskalets, Photonics Spectra8, 349 (2000).CAS Google Scholar

64. I. V. Krive, P. Sandstrom, R. I. Shekhter, S. M. Girvin, and M. Jonson, Phys. Rev. B 52, 16451 (1995). CrossRef Google Scholar

65. M. Pletyukhov and V. Gritsev, Phys. Rev. B 70, 165316 (2004). CrossRef Google Scholar

66. I. V. Krive, A. Palevski, R. I. Shekhter, and M. Jonson, Fiz. Nizk. Temp. 36, 155 (2010) I. V. Krive, A. Palevski, R. I. Shekhter, and M. Jonson,[Low Temp. Phys. 36, 119 (2010)]. CrossRef Google Scholar

67. E. N. Bogachek, G. A. Gogadze, and I. O. Kulik, Fiz. Nizk. Temp. 2, 461 (1976) E. N. Bogachek, G. A. Gogadze, and I. O. Kulik,[Sov. J. Low Temp. Phys. 2, 228 (1976)]. Google Scholar

68. E. N. Bogachek and I. O. Kulik, Fiz. Nizk. Temp. 9, 398 (1983) E. N. Bogachek and I. O. Kulik,[Sov. J. Low Temp. Phys. 9, 202 (1983)]. Google Scholar

69. E. N. Bogachek and U. Landman, Phys. Rev. B 50, 2678 (1994). CrossRef Google Scholar

70. V. Chandrasekhar, R. A. Webb, M. J. Brady, M. B. Ketchen, W. J. Gallagher, and A. Kleinsasser, Phys. Rev. Lett. 67, 3578 (1991). CrossRef Google Scholar

71. E. M. Q. Jariwala, P. Mohanty, M. B. Ketchen, and R. A. Webb, Phys. Rev. Lett. 86, 1594 (2001). CrossRef Google Scholar

72. L. P. Levy, Physica B 169, 245 (1991). CrossRef Google Scholar

73. D. Mally, C. Chapelier, and A. Benoit, Phys. Rev. Lett. 70, 2020 (1993). CrossRef Google Scholar

74. S. Washburn, H. Schmid, D. Kern, and R. A. Webb, Phys. Rev. Lett. 59, 1791 (1987). CrossRef Google Scholar

75. L. P. Levy, G. Golan, J. Dansmuir, and H. Bouchiat, Phys. Rev. Lett. 17, 2074 (1990). CrossRef Google Scholar

76. S. Pedersen, A. E. Hansen, C. B. Sorensen, and P. E. Lindelof, Phys. Rev. B 61, 5457 (2000). CrossRef Google Scholar

77. K. Tsubaki, Jpn. J. Appl. Phys. 40, 1902 (2001). CrossRef Google Scholar

78. N. O. Birge, Science 326, 244 (2009). CrossRef Google Scholar

79. A. C. Bleszynski-Jayich, W. B. Shanks, B. Peaudecerf, E. Ginossar, F. von Oppen, and J. G. E. Harris, Science 326, 272 (2009) and CrossRef Google Scholar

80. A. V. Balatsky and B. L. Altshuler, Phys. Rev. Lett. 70, 1678 (1993). CrossRef Google Scholar

81. A. Kamenev and Y. Gefen, Phys. Rev. B 49, 14474 (1999). CrossRef Google Scholar

82. Y. Gefen, Y. Imry, and M. Ya. Azbel, Phys. Rev. Lett. 52, 129 (1984). CrossRef Google Scholar

83. G. Montambaux, H. Bouchiat, D. Sigeti, and R. Friesner, Phys. Rev. B 42, 7647 (1990). CrossRef Google Scholar

84. B. L. Altshuler, Y. Gefen, and Y. Imry, Phys. Rev. Lett. 66, 88 (1991). CrossRef Google Scholar

85. J. R. Friedman and D. V. Averin, Phys. Rev. Lett. 88, 050403 (2002). CrossRef Google Scholar

86. D. V. Averin, Fortschr. Phys. 48, 1055 (2000). CrossRef Google Scholar

87. K. Likharev, in: Encyclopedia of Nanoscience and Nanotechnology 9, 865, H. S. Nalwa (ed.), American Sci. Publ. (2004). Google Scholar

88. K. von Klitzing, G. Dorda, and M. Pepper, Phys. Rev. Lett. 45, 494 (1980). CrossRef Google Scholar

89. R. B. Laughlin, Phys. Rev. B 23, 5632 (1981). CrossRef Google Scholar

90. D. Zanchi and G. Montambaux, Phys. Rev. Lett. 77, 366 (1996). CrossRef Google Scholar

91. U. Sivan and Y. Imry, Phys. Rev. Lett. 61, 1001 (1988). CrossRef Google Scholar

92. D. Loss, P. Goldbart, and A. V. Balatsky, Phys. Rev. Lett. 65, 1655 (1990). CrossRef Google Scholar

93. A. Stern, Phys. Rev. Lett. 68, 1022 (1992). CrossRef Google Scholar

94. Y. Aharonov and A. Stern, Phys. Rev. Lett. 69, 3593 (1992). CrossRef Google Scholar

95. D. Loss and P. M. Goldbart, Phys. Rev. B 45, 13544 (1992). CrossRef Google Scholar

96. I. O. Kulik, Physica B 284, 1880 (2000). CrossRef Google Scholar

97. I. O. Kulik, Persistent Current and Persistent Charge in Nanostructures, in Quantum Optics and the Spectroscopy of Solids, T. Hakioglu and A. S. Shumovsky (eds.), Kluver Acad. Publishers (1997). Google Scholar

98. I. O. Kulik, Physica B 218, 252 (1996). CrossRef Google Scholar

99. I. O. Kulik, T. Hakioglu, and A. Barone, Eur. Phys. J. B 30, 219 (2002). CrossRef Google Scholar

100. I. O. Kulik, Zh. Eksp. Teor. Fiz. 128, 1145 (2005) I. O. Kulik,[J. Exp. Theor. Phys. 101, 999 (2005)]. CrossRef Google Scholar

101. I. O. Kulik, Phys. Rev. B 76, 125313 (2007). CrossRef Google Scholar

102. E. Zipper and M. Szopa, Acta Phys. Pol. A 87, 79 (1995); E. Zipper and M. Szopa,Int. J. Mod. Phys. B 9, 161 (1994). Google Scholar

103. A. E. Allahverdyan and T. M. Nieuwenhuizen, Phys. Rev. Lett. 85, 1799 (2000). CrossRef Google Scholar

104. A. V. Nikulov, Phys. Rev. B64, 012505 (2001). CrossRef Google Scholar

105. D. J. Thouless, Phys. Rev. B 27, 6083 (1983). CrossRef Google Scholar

106. F. Zhou, B. Spivak, and B. Altshuler, Phys. Rev. Lett. 82, 608 (1999). CrossRef Google Scholar

107. B. Moskalets and M. Buttiker, Phys. Rev. B 66, 035306 (2002). CrossRef Google Scholar

108. M. Switkes, C. M. Marcus, K. Campman, and A. C. Gossard, Science 283, 1905 (1999). CrossRef Google Scholar

109. N. A. Sinitsyn and I. Nemenman, Phys. Rev. Lett. 99, 220408 (2007). CrossRef Google Scholar

110. V. Y. Chernyak and N. A. Sinitsyn, J. Chem. Phys. 131, 181101 (2009). CrossRef Google Scholar

111. T. Swahn, E. N. Bogachek, Yu. M. Galperin, M. Jonson, and R. I. Shekhter, Phys. Rev. Lett. 73, 162 (1994). CrossRef Google Scholar

112. I. E. Aronov, A. Grincwajg, M. Jonson, and R. I. Shekhter, Solid State Commun. 91, 75 (1994). CrossRef Google Scholar

113. E. N. Bogachek, Yu. M. Galperin, M. Jonson, R. I. Shekhter, and T. Swahn, J. Phys.: Condens. Matter 8, 2603 (1996). CrossRef Google Scholar

114. I. V. Krive, I. A. Romavsky, E. N. Bogachek, and U. Landman, Phys. Rev. Lett. 92, 126802 (2004). CrossRef Google Scholar

115. G. P. Berman, E. N. Bulgakov, D. K. Campbell, and I. V. Krive, Phys. Rev. B 56, 10338 (1997). CrossRef Google Scholar

116. Y. Makhlin and A. D. Mirlin, Phys. Rev. Lett. 87, 276803 (2001). CrossRef Google Scholar

117. J. Mateo and J. M. Cervero, J. Phys. A 37, 2465 (2004). CrossRef Google Scholar

118. M. Y. Choi, Phys. Rev. Lett. 71, 2987 (1993). CrossRef Google Scholar

119. D. Loss and T. Martin, Phys. Rev. B 47, 4619 (1993). CrossRef Google Scholar

120. S. Yip, Phys. Rev. B 52, 3087 (1995). CrossRef Google Scholar

121. Yu. A. Kolesnichenko, A. N. Omelyanchouk, and S. N. Shevchenko, Fiz. Nizk. Temp. 30, 288 (2004) Yu. A. Kolesnichenko, A. N. Omelyanchouk, and S. N. Shevchenko,[Low Temp. Phys. 30, 213 (2004)]. CrossRef Google Scholar

122. Yu. A. Kolesnichenko, A. N. Omelyanchouk, and A. M. Zagoskin, Fiz. Nizk. Temp. 30, 714 (2004) Yu. A. Kolesnichenko, A. N. Omelyanchouk, and A. M. Zagoskin,[Low Temp. Phys. 30, 535 (2004)]. CrossRef Google Scholar

123. E. N. Bogachek, G. A. Gogadze, and I. O. Kulik, Phys. Status Solidi B67, 287 (1975). CrossRef Google Scholar

124. T.-C. Wei and P. M. Goldbart, Phys. Rev. B 77, 224512 (2008). CrossRef Google Scholar

125. X. Zhang and J. C. Price, Phys. Rev. B 55, 3128 (1997). CrossRef Google Scholar

126. A. Ferretti, I. O. Kulik, and A. Lami, Phys. Rev. B 47, 12235 (1993). CrossRef Google Scholar

127. K. Czajka, M. M. Maska, M. Mierzjewski, and Z. Sledz, Phys. Rev. B 72, 035320 (2005). CrossRef Google Scholar

128. S. V. Sharov and A. D. Zaikin, Phys. Rev. B 71, 014518 (2005). CrossRef Google Scholar

129. J. Dajka, L. Machura, S. Rogozinski, and J. Luczka, Phys. Status Solidi B 7, 2432 (2007). CrossRef Google Scholar

130. J. Dajka, S. Rogozinski, L. Machura, and J. Luczka, Acta Phys. Pol. B 38, 1737 (2007).CAS Google Scholar

131. F. Loder, A. P. Kampf, T. Kopp, J. Mannhart, C. W. Schneider, and Y. S. Barash, Nat. Phys., Adv. Online Publication 1, (2007). Google Scholar

132. F. Loder, A. P. Kampf, and T. Kopp, Phys. Rev. B 78, 174526 (2008). CrossRef Google Scholar

133. V. Juricic, I. F. Herbut, and Z. Tesanovic, Phys. Rev. Lett. 100, 187006 (2008). CrossRef Google Scholar

134. V. Vakaryuk, Phys. Rev. Lett. 101, 167002 (2008). CrossRef Google Scholar

135. Geometric Phases in Physics, in: Adv. Series in Physics, A. Shapere and F. Wilczek (eds.), World Scientific, Singapore (1989). Google Scholar

136. R. Onur Umucalilar, Berry’s Phase (unpublished). Google Scholar

137. K. A. Matveev, A. I. Larkin, and L. I. Glazman, Phys. Rev. Lett. 89, 096802 (2002). CrossRef Google Scholar

138. D. Gatteschi, A. Caneschi, L. Pardi, and R. Sessoli, Science 265, 1054 (1994). CrossRef Google Scholar

139. K. L. Taft, C. D. Delfs, G. C. Papaefthymiou, S. Foner, D. Gatteschi, and J. Lippard, J. Am. Chem. Soc. 116, 823 (1994). CrossRef Google Scholar

140. S. V. Sharov and A. D. Zaikin, Photonics Spectra 29, 360 (2005). CrossRef Google Scholar

141. V. E. Kravtsov and M. R. Zirnbauer, Phys. Rev. B 46, 4332 (1992). CrossRef Google Scholar