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Thermal Amplitude Fluctuations in Arrays of Small Josephson Junctions

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Abstract

In studies on Josephson Junctions arrays (JJA), it is usually assumed that finite size effects enter only through the grain capacitance and that the amplitude of the superconducting gap is well described by the bulk Bardeeen–Cooper–Schrieber (BCS) prediction. Here, we employ path integral techniques to show analytically that for sufficiently small grains thermal fluctuations modify substantially the amplitude of the order parameter and the critical temperature of the JJA. We identify a region of sizes and temperatures for which quantum fluctuations are negligible and thermal fluctuations enhance the critical temperature of the JJA.

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References

  1. Josephson, B.D.: Phys. Lett. 1, 251 (1962)

    Article  ADS  MATH  Google Scholar 

  2. Eley, S., Gopalakrishnan, S., Goldbart, P.M., Mason, N.: Nat. Phys. 8, 59 (2012)

    Article  Google Scholar 

  3. Orr, B.G., Jaeger, H.M., Goldman, A.M., Kuper, C.G.: Phys. Rev. Lett. 56, 378 (1986)

    Article  ADS  Google Scholar 

  4. Jaeger, H.M., Haviland, D.B., et al.: Phys. Rev. B 40, 182 (1989)

    Article  ADS  Google Scholar 

  5. Ambegaokar, V., Eckern, U., Schon, G.: Phys. Rev. Lett. 48, 1745 (1982)

    Article  ADS  Google Scholar 

  6. Caldeira, A.D., Leggett, A.J.: Phys. Rev. Lett. 48, 1571 (1982)

    Article  ADS  Google Scholar 

  7. Ghosal, A., Randeria, M., Trivedi, N.: Phys. Rev. B 65, 014501 (2001)

    Article  ADS  Google Scholar 

  8. Lang, K.M., Madhavan, V., et al.: Nature 415, 412 (2002)

    Article  ADS  Google Scholar 

  9. Abeles, B.: Phys. Rev. B 15, 2828 (1973)

    Article  ADS  Google Scholar 

  10. Merchant, L., Ostrick, J., et al.: Phys. Rev. B 63, 134508 (2001)

    Article  ADS  Google Scholar 

  11. Chakravarty, S., Ingold, G.L., et al.: Phys. Rev. Lett. 56, 2303 (1986)

    Article  ADS  Google Scholar 

  12. Beloborodov, I.S., Lopatin, A.V., et al.: Rev. Mod. Phys. 79, 469 (2007)

    Article  ADS  Google Scholar 

  13. Efetov, K.B.: Sov. Phys. JETP 52, 568 (1980)

    ADS  Google Scholar 

  14. Bradley, R.M., Doniach, S.: Phys. Rev. B 30, 1138 (1984)

    Article  ADS  Google Scholar 

  15. Fisher, M.P.A.: Phys. Rev. B 36, 1917 (1987)

    Article  ADS  Google Scholar 

  16. Zaikin, A.D., Golubev, D.S., et al.: Phys. Rev. Lett. 78, 1552 (1997)

    Article  ADS  Google Scholar 

  17. Buchler, H.P., Geshkenbein, V.B., Blatter, G.: Phys. Rev. Lett. 92, 067007 (2004)

    Article  ADS  Google Scholar 

  18. Kosterlitz, J.M., Thouless, D.J.: J. Phys. C, Solid State Phys. 6, 1181 (1973)

    Article  ADS  Google Scholar 

  19. Chakravarty, S., et al.: Phys. Rev. B 35, 7256 (1987)

    Article  ADS  Google Scholar 

  20. Kampf, A., Schoen, G.: Phys. Rev. B 36, 3651 (1987)

    Article  ADS  Google Scholar 

  21. Bose, S., et al.: Nat. Mater. 9, 550 (2010)

    Article  ADS  Google Scholar 

  22. Brihuega, I., et al.: Phys. Rev. B 84, 104525 (2011)

    Article  ADS  Google Scholar 

  23. Eley, S., et al.: Nat. Phys. 8, 59 (2012)

    Article  Google Scholar 

  24. Ricci, A., et al.: Phys. Rev. B 84, 060511 (2011)

    Article  ADS  Google Scholar 

  25. Muhlschlegel, B., Scalapino, D.J., Denton, R.: Phys. Rev. B 6, 1767 (1972)

    Article  ADS  Google Scholar 

  26. Ambegaokar, V., Baratoff, A.: Phys. Rev. Lett. 10, 486 (1963)

    Article  ADS  Google Scholar 

  27. Ribeiro, P., Garcia-Garcia, A.M.: Phys. Rev. Lett. 108, 097004 (2012)

    Article  ADS  Google Scholar 

  28. Larkin, A., Varlamov, A.: Theory of Fluctuations in Superconductors. Clarendon, Oxford (2005)

    Book  MATH  Google Scholar 

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Acknowledgements

We thank Pedro Ribeiro for illuminating discussions.

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Correspondence to Antonio M. García-García.

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García-García, A.M. Thermal Amplitude Fluctuations in Arrays of Small Josephson Junctions. J Supercond Nov Magn 26, 2693–2695 (2013). https://doi.org/10.1007/s10948-013-2162-z

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  • DOI: https://doi.org/10.1007/s10948-013-2162-z

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