Skip to main content

Fluctuation Modes in Multi-gap Superconductors

  • Chapter
  • First Online:
Book cover Vortices and Nanostructured Superconductors

Part of the book series: Springer Series in Materials Science ((SSMATERIALS,volume 261))

  • 717 Accesses

Abstract

We investigate excitation modes in multi-gap superconductors. Multi-gap superconductors have multiple excitation modes. In particular, the Nambu-Goldstone mode , Leggett mode and Higgs modes are important and play an important role in multi-gap superconductors. The multiple-phase invariance in a multi-gap system is partially or totally spontaneously broken in a superconductor. We evaluate the dispersion relation and the mass formulas of these modes by using the functional-integral method. The broken multiple-phase invariance leads to a new quantum phase such as the time-reversal symmetry breaking , the emergence of massless modes and fractionally quantized-flux vortices. There is a possibility that half-flux vortices exist in a two-component superconductor in magnetic field .

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 99.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 129.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 129.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. V.A. Moskalenko, Fiz. Metal Metallored 8, 2518 (1959)

    Google Scholar 

  2. H. Suhl, B.T. Mattis, L.W. Walker, Phys. Rev. Lett. 3, 552 (1959)

    Article  ADS  Google Scholar 

  3. J. Peretti, Phys. Lett. 2, 275 (1962)

    Article  ADS  Google Scholar 

  4. J. Kondo, Prog. Theor. Phys. 29, 1 (1963)

    Article  ADS  Google Scholar 

  5. J. Bardeen, L. Cooper, R. Schrieffer, Phys. Rev. 106, 162 (1957)

    Article  ADS  MathSciNet  Google Scholar 

  6. G. Binning, A. Baratoff, H.E. Hoenig, J.G. Bednorz, Phys. Rev. Lett. 45, 1352 (1980)

    Article  ADS  Google Scholar 

  7. L. P. Gorkov, arXiv:1508.00529

  8. S.V. Shulga et al., Phys. Rev. Lett. 80, 1730 (1998)

    Article  ADS  Google Scholar 

  9. J. Nagamatsu, N. Nakagawa, T. Muranaka, Y. Zenitani, J. Akimitsu, Nature 410, 63 (2001)

    Article  ADS  Google Scholar 

  10. Y. Kamihara, T. Watanabe, M. Hirano, H. Hosono, J. Ame. Chem. Soc. 130, 3296 (2008)

    Article  Google Scholar 

  11. K.H. Bennemann, J.B. Ketterson (eds.), The Physics of Superconductors (Springer-Verlag, Berlin, 2004)

    Google Scholar 

  12. A. Bianconi, Nat. Phys. 9, 536 (2013)

    Google Scholar 

  13. A. Bianconi, A.C. Castellano, M. De, Santis, P. Delogu, A. Garano and R. Giorgi. Solid State Commun. 63, 1135 (1987)

    Article  ADS  Google Scholar 

  14. The Physics of superconductors, vols. I and II, ed. by K.H. Bennemann, J.B. Ketterson (Springer, Berlin, 2003)

    Google Scholar 

  15. V.J. Emery, Phys. Rev. Lett. 58, 2794 (1987)

    Article  ADS  Google Scholar 

  16. J.E. Hirsch, D. Loh, D.J. Scalapino, S. Tang, Phys. Rev. B 39, 243 (1989)

    Article  ADS  Google Scholar 

  17. K. Yamaji et al., Physica C 304, 225 (1998)

    Article  ADS  Google Scholar 

  18. T. Yanagisawa, S. Koike, K. Yamaji, Phys. Rev. B 64, 184509 (2001)

    Article  ADS  Google Scholar 

  19. T. Yanagisawa, S. Koike, K. Yamaji, Phys. Rev. B 67, 132408 (2003)

    Article  ADS  Google Scholar 

  20. C. Weber, A. Lauchi, G.A. Sawatzky, Phys. Rev. Lett. 102, 017005 (2009)

    Article  ADS  Google Scholar 

  21. T. Yanagisawa, J. Phys. Soc. Jpn. 85, 114707 (2016)

    Article  ADS  Google Scholar 

  22. S. Koike et al., J. Phys. Soc. Jpn. 68, 1657 (1999)

    Article  ADS  Google Scholar 

  23. K. Yamaji et al., Physica C 235, 2221 (1994)

    Article  ADS  Google Scholar 

  24. T. Yanagisawa, Y. Shimoi, K. Yamaji, Phys. Rev. B 52, R3860 (1995)

    Article  ADS  Google Scholar 

  25. A. Bussmann-Holder, H. Keller, R. Khasanov, A. Simon, A. Bianconi, A.R. Bishop, New J. Phys. 13, 093009 (2011)

    Article  ADS  Google Scholar 

  26. H.Y. Choi et al., Phys. Rev. B 80, 052505 (2009)

    Article  ADS  Google Scholar 

  27. P.M. Shirage, K. Kihou, K. Miyazawa, C.-H. Lee, H. Kito, H. Eisaki, T. Yanagisawa, Y. Tanaka, A. Iyo. Phys. Rev. Lett. 103, 257003 (2009)

    Article  ADS  Google Scholar 

  28. T. Yanagisawa, K. Odagiri, I. Hase, K. Yamaji, P.M. Shirage, Y. Tanaka, A. Iyo, H. Eisaki, J. Phys. Soc. Jpn. 78, 094718 (2009)

    Article  ADS  Google Scholar 

  29. A.D. Hillier, J. Quintanilla, R. Cywinskii, Phys. Rev. Lett. 102, 117007 (2009)

    Article  ADS  Google Scholar 

  30. I. Hase, T. Yanagisawa, J. Phys. Soc. Jpn. 78, 084724 (2009)

    Article  ADS  Google Scholar 

  31. A.D. Hillier, J. Quintanilla, B. Mazidian, J.F. Annett, R. Cywinskii, Phys. Rev. Lett. 109, 097001 (2012)

    Article  ADS  Google Scholar 

  32. I. Hase, T. Yanagisawa, J. Phys. Soc. Jpn. 81, 103704 (2012)

    Article  ADS  Google Scholar 

  33. D.J. Singh, Phys. Rev. B 86, 174507 (2012)

    Article  ADS  Google Scholar 

  34. V.K. Pecharsky, L.L. Miller, K.A. Gschneider, Phys. Rev. B 58, 497 (1998)

    Article  ADS  Google Scholar 

  35. Y. Iwamoto, Y. Iwasaki, K. Ueda, T. Kohara, Phys. Lett. A 250, 439 (1998)

    Article  ADS  Google Scholar 

  36. H.H. Sung, S.Y. Chou, K.J. Syu, W.H. Lee, J. Phys. COndens. Matter 20, 165207 (2008)

    Article  ADS  Google Scholar 

  37. S. Katano et al., Phys. Rev. B 90, 220508 (2014)

    Article  ADS  Google Scholar 

  38. V. Stanev, Z. Tesanovic, Phys. Rev. B 81, 134522 (2010)

    Article  ADS  Google Scholar 

  39. Y. Tanaka, T. Yanagisawa, J. Phys. Soc. Jpn. 79, 114706 (2010)

    Article  ADS  Google Scholar 

  40. Y. Tanaka, T. Yanagisawa, Solid State Commun. 150, 1980 (2010)

    Article  ADS  Google Scholar 

  41. R.G. Dias, A.M. Marques, Supercond. Sci. Technol. 24, 085009 (2011)

    Article  ADS  Google Scholar 

  42. T. Yanagisawa, Y. Tanaka, I. Hase, K. Yamaji, J. Phys. Soc. Jpn. 81, 024712 (2012)

    Article  ADS  Google Scholar 

  43. X. Hu, Z. Wang, Phys. Rev. B 85, 064516 (2012)

    Article  ADS  Google Scholar 

  44. V. Stanev, Phys. Rev. B 85, 174520 (2012)

    Article  ADS  Google Scholar 

  45. C. Platt, R. Thomale, C. Homerkamp, S.C. Zhang, Phys. Rev. B 85, 180502 (2012)

    Article  ADS  Google Scholar 

  46. S. Maiti, A.V. Chubukov, Phys. Rev. B 87, 144511 (2013)

    Article  ADS  Google Scholar 

  47. B.J. Wilson, M.P. Das, J. Phys. Condens. Matter 25, 425702 (2013)

    Article  ADS  Google Scholar 

  48. Y. Takahashi, Z. Huang, X. Hu, J. Phys. Soc. Jpn. 83, 034701 (2014)

    Article  ADS  Google Scholar 

  49. R. Ganesh, G. Baskaran, J. van den Brink, D.V. Efremov, Phys. Rev. Lett. 113, 177001 (2014)

    Article  ADS  Google Scholar 

  50. Y. S. Yerin, A. N. Omelyanchouk and E. ll’chev, arXiv:1503.04653 (2015)

  51. T. Yanagisawa, I. Hase, J. Phys. Soc. Jpn. 82, 124704 (2013)

    Article  ADS  Google Scholar 

  52. S.Z. Lin, X. Hu, New J. Phys. 14, 063021 (2012)

    Article  ADS  Google Scholar 

  53. K. Kobayashi, M. Machida, Y. Ota, F. Nori, Phys. Rev. B 88, 224516 (2013)

    Article  ADS  Google Scholar 

  54. T. Koyama, J. Phys. Soc. Jpn. 83, 074715 (2014)

    Article  ADS  Google Scholar 

  55. T. Yanagisawa, Y. Tanaka, New J. Phys. 16, 123014 (2014)

    Article  ADS  Google Scholar 

  56. Y. Tanaka et al., Physica C 516, 10 (2015)

    Article  ADS  Google Scholar 

  57. S.-Z. Lin, X. Hu, Phys. Rev. Lett. 108, 177005 (2012)

    Article  ADS  Google Scholar 

  58. YuA Izyumov, V.M. Laptev, Phase Transitions 20, 95 (1990)

    Article  Google Scholar 

  59. G.E. Volovik, The Universe in a Helium Droplet (Oxford University Press, Oxford, 2009)

    Book  Google Scholar 

  60. Y. Tanaka, Phys. Rev. Lett. 88, 017002 (2002)

    Article  ADS  Google Scholar 

  61. E. Babaev, Phys. Rev. Lett. 89, 067001 (2002)

    Article  ADS  Google Scholar 

  62. S.V. Kuplevakhsky, A.N. Omelyanchouk, Y.S. Yerin, J. Low Temp. Phys. 37, 667 (2011)

    Article  Google Scholar 

  63. A.J. Leggett, Prog. Theor. Phys. 36, 901 (1966)

    Article  ADS  Google Scholar 

  64. Y. Tanaka et al., Physica C 471, 747 (2011)

    Article  ADS  Google Scholar 

  65. V. Moshchalkov et al., Phys. Rev. Lett. 102, 117001 (2009)

    Article  ADS  Google Scholar 

  66. M. Silaev, E. Babaev, Phys. Rev. B 84, 094515 (2011)

    Article  ADS  Google Scholar 

  67. Y. Nambu, Phys. Rev. 117, 648 (1960)

    Article  ADS  MathSciNet  Google Scholar 

  68. Y. Nambu, in Physics in the 21st Century edited by K, ed. by H. Kunitomo, H. Otsubo (World Scientific, Singapore, Kikkawa, 1997)

    Google Scholar 

  69. T. Yanagisawa, Novel Supercon. Materials 1, (2015)

    Google Scholar 

  70. B. T. Geilikman, R. O. Zaitsev and V. Z. Kresin, Sov. Phys.: Solid State 9642, (1967)

    Google Scholar 

  71. D.R. Tilley, Proc. Phys. Soc. 84, 573 (1964)

    Article  ADS  MathSciNet  Google Scholar 

  72. I.P. Ivanov, Phys. Rev. E 79, 021116 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  73. N.V. Orlova, A.A. Shanenko, M.V. Milosevic, F.M. Peeters, A. V. Vagov ad V. M. Axt. Phys. Rev. B 87, 134510 (2013)

    Article  ADS  Google Scholar 

  74. Z. Huang, X. Hu, Appl. Phys. Lett. 104, 162602 (2014)

    Article  ADS  Google Scholar 

  75. Y.S. Yerin, A.N. Omelyanchouk, Low Temp. Phys. 40, 943 (2014)

    Article  ADS  Google Scholar 

  76. Y. Tanaka, Super. Sci. Tech. 28, 034002 (2015)

    Article  ADS  Google Scholar 

  77. J.G. Storey, J.W. Loram, J.R. Cooper, Z. Bukowski, J. Karpinski, Phys. Rev. B 88, 144502 (2013)

    Article  ADS  Google Scholar 

  78. R.G. Cai, L. Li, L.F. Li, Y.Q. Wang, JHEP 9, 074 (2013)

    Article  ADS  Google Scholar 

  79. W.-Y. Wen, M.-S. Wu, S.-Y. Wu, Phys. Rev. D 89, 066005 (2014)

    Article  ADS  Google Scholar 

  80. M. Nishida, JHEP 08, 136 (2015)

    Article  Google Scholar 

  81. R. Rajaraman, Solitons and Instantons (North-Holland, Elsevier, Amsterdam, 1987)

    MATH  Google Scholar 

  82. Y. Tanaka, J. Phys. Soc. Jpn. 70, 2844 (2001)

    Article  ADS  Google Scholar 

  83. E. Babaev, L.D. Faddeev, A.J. Niemi, Phys. Rev. B 65, 100512 (2002)

    Article  ADS  Google Scholar 

  84. Y.M. Cho, P. Zhang, Phys. Rev. B 73, 180506 (2006)

    Article  ADS  Google Scholar 

  85. M. Eto, Y. Hirono, M. Nitta and S. Yasui, Prog. Theor. Exp. Phys. 012D01 (2014)

    Google Scholar 

  86. M.C.N. Fiolhais, J.L. Birman, Phys. Lett. A 378, 2632 (2014)

    Article  ADS  Google Scholar 

  87. E. Babaev, M. Speight, Phys. Rev. B 72, 180502 (2005)

    Article  ADS  Google Scholar 

  88. V.G. Kogan, J. Schmalian, Phys. Rev. B 83, 054515 (2011)

    Article  ADS  Google Scholar 

  89. E. Babaev, M. Silaev, Phys. Rev. B 86, 016501 (2012)

    Article  ADS  Google Scholar 

  90. V.G. Kogan, J. Schmalian, Phys. Rev. B 86, 016502 (2012)

    Article  ADS  Google Scholar 

  91. M. Marciani, L. Fanfarillo, C. Castellani, L. Benfatto, Phys. Rev. B 88, 214508 (2013)

    Article  ADS  Google Scholar 

  92. T. Yanagisawa, EPL 113, 41001 (2016)

    Article  ADS  Google Scholar 

  93. R. Kleiner, F. Steinmeyer, G. Kunkel, P. Muller, Phys. Rev. Lett. 68, 2349 (1992)

    Article  Google Scholar 

  94. G. Ohya, N. Aoyama, A. Irie, S. Kishida, H. Tokutaka, Jpn. J. Appl. Phys. 31, L829 (1992)

    Article  Google Scholar 

  95. K. Tamasaku, Y. Nakamura, S. Uchida, Phys. Rev. Lett. 69, 1455 (1992)

    Article  ADS  Google Scholar 

  96. Y. Matsuda, M.B. Gaifullin, K. Kumagai, K. Kadowaki, T. Mochiku, Phys. Rev. Lett. 75, 4512 (1995)

    Article  ADS  Google Scholar 

  97. T. Koyama, M. Tachiki, Phys. Rev. B 54, 16183 (1996)

    Article  ADS  Google Scholar 

  98. S.G. Sharapov, V.P. Gusynin, H. Beck, Eur. Phys. J. B 39, 062001 (2002)

    Google Scholar 

  99. H.J. Choi, D. Roundy, H. Sun, M.L. Cohen, S.G. Louie, Nature 418, 758 (2002)

    Article  ADS  Google Scholar 

  100. G. Blumberg et al., Phys. Rev. Lett. 99, 014507 (2007)

    Article  Google Scholar 

  101. Y. Ota, M. Machida, T. Koyama, H. Aoki, Phys. Rev. B 83, 060507 (2011)

    Article  ADS  Google Scholar 

  102. R. Matsunaga, Y.I. Hamada, K. Makise, Y. Uzawa, H. Terai, Z. Wang, R. Shimano, Phys. Rev. Lett. 111, 057002 (2013)

    Article  ADS  Google Scholar 

  103. M.A. Measson, Y. Gallais, M. Cazayous, B. Clair, P. Rodiere, L. Cario, A. Sacuto, Phys. Rev. B 89, 060503 (2014)

    Article  ADS  Google Scholar 

  104. Y. Barlas, C.M. Varma, Phys. Rev. B 87, 054503 (2013)

    Article  ADS  Google Scholar 

  105. T. Koyama, Phys. Rev. B 90, 064514 (2014)

    Article  ADS  Google Scholar 

  106. N. Tsuji, H. Aoki, Phys. Rev. B 92, 064508 (2015)

    Article  ADS  Google Scholar 

  107. Y. Nambu, G. Jona-Lasinio, Phys. Rev. 122, 345 (1961)

    Article  ADS  Google Scholar 

  108. Y. Nambu, G. Jona-Lasinio, Phys. Rev. 124, 246 (1961)

    Article  ADS  Google Scholar 

  109. Y. Nambu, Physica D 15, 147 (1985)

    Article  ADS  Google Scholar 

  110. T. Koyama, J. Phys. Soc. Jpn. 88, 064715 (2016)

    Article  ADS  Google Scholar 

  111. U. Welp et al., Phys. Rev. B 78, 140510 (R) (2008)

    Google Scholar 

  112. A. Gurevich, V. Vinokur, Phys. Rev. Lett. 90, 047004 (2003)

    Article  ADS  Google Scholar 

  113. H.-Y. Kee, Y.B. Kim, K. Maki, Phys. Rev. B 62, R9275 (2000)

    Article  ADS  Google Scholar 

  114. J. Jang et al., Science 331, 186 (2011)

    Article  ADS  Google Scholar 

  115. M. Nitta, M. Eto, T. Fujimori, T. Ohashi, J. Phys. Soc. Jpn. 81, 084711 (2012)

    Article  ADS  Google Scholar 

  116. K.G. Wilson, J.B. Kogut, Phys. Rep. 12C, 75 (1974)

    Article  ADS  Google Scholar 

  117. J.B. Kogut, Rev. Mod. Phys. 51, 659 (1979)

    Article  ADS  Google Scholar 

  118. C. Chakravarty, B.I. Halperin, D.R. Nelson, Phys. Rev. B 39, 2344 (1989)

    Article  ADS  Google Scholar 

  119. T. Yanagisawa, Phys. Rev. B 46, 13896 (1992)

    Article  ADS  Google Scholar 

  120. J.M. Kosterlitz, D. Thouless, J. Phys. C 6, 1181 (1973)

    Google Scholar 

  121. J. Zinn-Justin, Quantum Field Theory and Critical Phenomena (Oxford University Press, Oxford, 1989)

    MATH  Google Scholar 

  122. D.J. Amit, Y.Y. Goldschmidt, S. Grinstein, J. Phys. A: Math. Gen. 13, 585 (1980)

    Article  ADS  Google Scholar 

  123. T.A. Bojesen, E. Babaev, A. Sudbo, Phys. Rev. B 88, 220511 (2013)

    Article  ADS  Google Scholar 

  124. Y. Tanaka et al., J. Phys. Soc. Jpn. 83, 074705 (2014)

    Article  ADS  Google Scholar 

  125. S. Miyashita, H. Shiba, J. Phys. Soc. Jpn. 53, 1145 (1984)

    Article  ADS  Google Scholar 

  126. D.J. Gross, E. Witten, Phys. Rev. D 21, 446 (1980)

    Article  ADS  Google Scholar 

  127. E. Brezin, D.J. Gross, Phys. Lett. B 97, 120 (1980)

    Article  ADS  MathSciNet  Google Scholar 

  128. R.C. Brower, M. Nauenberg, Nucl. Phys. B 180, 221 (1981)

    Article  ADS  Google Scholar 

  129. E. Brezin, S. Hikami, JHEP 7, 67 (2010)

    Article  ADS  Google Scholar 

  130. M. Nitta, Nucl. Phys. B 895, 288 (1995)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

The author expresses his sincere thanks to J. Kondo, K. Yamaji, I. Hase and Y. Tanaka for helpful discussions.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Takashi Yanagisawa .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this chapter

Cite this chapter

Yanagisawa, T. (2017). Fluctuation Modes in Multi-gap Superconductors . In: Crisan, A. (eds) Vortices and Nanostructured Superconductors. Springer Series in Materials Science, vol 261. Springer, Cham. https://doi.org/10.1007/978-3-319-59355-5_8

Download citation

Publish with us

Policies and ethics