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Fractional ac Josephson effect in p- and d-wave superconductors

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Abstract

For certain orientations of Josephson junctions between two p x -wave or two d-wave superconductors, the subgap Andreev bound states produce a \(4\pi\)-periodic relation between the Josephson current I and the phase difference \(\phi\): \(I\propto\sin(\phi/2)\). Consequently, the ac Josephson current has the fractional frequency \(eV/\hbar\), where V is the dc voltage. In the tunneling limit, the Josephson current is proportional to the first power (not square) of the electron tunneling amplitude. Thus, the Josephson current between unconventional superconductors is carried by single electrons, rather than by Cooper pairs. The fractional ac Josephson effect can be observed experimentally by measuring frequency spectrum of microwave radiation from the junction. We also study junctions between singlet s-wave and triplet p x -wave, as well as between chiral \(p_x\pm ip_y\)-wave superconductors.

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References

  1. D.J. van Harlingen, Rev. Mod. Phys. 67, 515 (1995); C. Tsuei, J. Kirtley, Rev. Mod. Phys. 72, 969 (2000)

    Article  ADS  Google Scholar 

  2. TMTSF stands for tetramethyltetraselenafulvalene, and X represents inorganic anions such as \(\rm ClO_4\) or \(\rm PF_6\)

  3. I.J. Lee, S.E. Brown, W.G. Clark, M.J. Strouse, M.J. Naughton, W. Kang, P.M. Chaikin, Phys. Rev. Lett. 88, 017004 (2002); I.J. Lee, M.J. Naughton, G.M. Danner, P.M. Chaikin, Phys. Rev. Lett. 78, 3555 (1997); I.J. Lee, P.M. Chaikin, M.J. Naughton, Phys. Rev. B 62, R14669 (2000)

    Article  ADS  Google Scholar 

  4. A.A. Abrikosov, J. Low Temp. Phys. 53, 359 (1983)

    Article  ADS  Google Scholar 

  5. A.G. Lebed, Phys. Rev. B 59, R721 (1999); A.G. Lebed, K. Machida, M. Ozaki, Phys. Rev. B 62, R795 (2000)

  6. Y. Maeno, T.M. Rice, M. Sigrist, Phys. Today 54, 42 (2001); Y. Maeno, T.M. Rice, M. Sigrist, Phys. Today Erratum 54, 104 (2001); A.P. Mackenzie, Y. Maeno, Rev. Mod. Phys. 75, 657 (2003)

    Article  ADS  Google Scholar 

  7. P.G. de Gennes, D. Saint-James, Phys. Lett. 4, 151 (1963); A.F. Andreev, Zh. Eksp. Teor. Fiz. 49, 655 (1965) [Sov. Phys. JETP 22, 455 (1966)]

    Article  ADS  MATH  Google Scholar 

  8. C. Bruder, Phys. Rev. B 41, 4017 (1990)

    Article  ADS  Google Scholar 

  9. C.-R. Hu, Phys. Rev. Lett. 72, 1526 (1994)

    Article  ADS  Google Scholar 

  10. S. Kashiwaya, Y. Tanaka, Rep. Prog. Phys. 63, 1641 (2000)

    Article  ADS  Google Scholar 

  11. K. Sengupta, I. Žutić, H.-J. Kwon, V.M. Yakovenko, S. Das Sarma, Phys. Rev. B 63, 144531 (2001)

    Article  ADS  Google Scholar 

  12. Y. Tanuma, K. Kuroki, Y. Tanaka, S. Kashiwaya, Phys. Rev. B 64, 214510 (2001); Y. Tanuma, K. Kuroki, Y. Tanaka, R. Arita, S. Kashiwaya, H. Aoki, Phys. Rev. B 66, 094507 (2002)

    Article  ADS  Google Scholar 

  13. C. Honerkamp, M. Sigrist, J. Low T. Phys. 111, 895 (1998); M. Matsumoto, M. Sigrist, J. Phys. Soc. Jpn 68, 994 (1999)

    Article  ADS  Google Scholar 

  14. K. Sengupta, H.-J. Kwon, V.M. Yakovenko, Phys. Rev. B 65, 104504 (2002)

    Article  ADS  Google Scholar 

  15. H.-J. Kwon, V.M. Yakovenko, K. Sengupta, Synth. Metals 133-134, 27 (2003)

    Google Scholar 

  16. I.O. Kulik, Zh. Eksp. Teor. Fiz. 57, 1745 (1969) [Sov. Phys. JETP 30, 944 (1970)]; C. Ishii, Progr. Theor. Phys. 44, 1525 (1970); J. Bardeen, J.L. Johnson, Phys. Rev. B 5, 72 (1972)

    Google Scholar 

  17. T. Löfwander, V.S. Shumeiko, G. Wendin, Supercond. Sci. Technol. 14, R53 (2001)

  18. Y. Tanaka, T. Hirai, K. Kusakabe, S. Kashiwaya, Phys. Rev. B 60, 6308 (1999)

    Article  ADS  Google Scholar 

  19. C.D. Vaccarella, R.D. Duncan, C.A.R. Sá de Melo, Physica C 391, 89 (2003)

    Article  ADS  Google Scholar 

  20. A.F. Andreev, Zh. Eksp. Teor. Fiz. 46, 1823 (1964) [Sov. Phys. JETP 19, 1228 (1964)]

    Google Scholar 

  21. M. Nishida, N. Hatakenaka, S. Kurihara, Phys. Rev. Lett. 88, 145302 (2002)

    Article  ADS  Google Scholar 

  22. The current-phase relation \(I\propto\sin(\phi/2)\) that we propose should not be confused with another unconventional current-phase relation \(I\propto\sin(2\phi)\) with the period \(\pi\), which was predicted theoretically for junctions between s- and d-wave superconductors [29, 43, 44], s- and p-wave superconductors [29-31], and for the \(0^\circ/45^\circ\) junctions between two d-wave superconductors [42]

  23. Y. Tanaka, S. Kashiwaya, Phys. Rev. B 56, 892 (1997)

    Article  ADS  Google Scholar 

  24. R.A. Riedel, P.F. Bagwell, Phys. Rev. B 57, 6084 (1998)

    Article  ADS  Google Scholar 

  25. Yu.S. Barash, Phys. Rev. B 61, 678 (2000)

    Article  ADS  Google Scholar 

  26. H.-J. Kwon, K. Sengupta, V.M. Yakovenko, Brazil. J. Phys. 33, 653 (2003)

    Article  Google Scholar 

  27. A.Yu. Kitaev, arXiv: cond-mat/0010440

  28. Yu.S. Barash, A.M. Bobkov, M. Fogelström, Phys. Rev. B 64, 214503 (2001)

    Article  ADS  Google Scholar 

  29. S. Yip, J. Low T. Phys. 91, 203 (1993).

    Article  ADS  Google Scholar 

  30. N. Yoshida, Y. Tanaka, S. Kashiwaya, J. Inoue, J. Low T. Phys. 117, 563 (1999)

    Article  ADS  Google Scholar 

  31. Y. Asano, Y. Tanaka, M. Sigrist, S. Kashiwaya, Phys. Rev. B 67, 184505 (2003)

    Article  ADS  Google Scholar 

  32. A.J. Leggett, Rev. Mod. Phys. 47, 331 (1975)

    Article  ADS  Google Scholar 

  33. A.M. Zagoskin, Quantum Theory of Many-Body Systems (Springer, New York, 1998)

  34. A. Furusaki, Superlatt. Microstruct. 25, 809 (1999)

    Article  ADS  Google Scholar 

  35. Y. Tanaka, S. Kashiwaya, Phys. Rev. B 53, 9371 (1996)

    Article  ADS  Google Scholar 

  36. Equation (15) can be equivalently obtained as a difference between the right- and left-moving currents using the formula I a =ev F (|A a |2−|B a |2) with the normalization condition \(\int dx |\psi^2|=1\) [34]

  37. V. Ambegaokar, A. Baratoff, Phys. Rev. Lett. 10, 486 (1963); erratum 11, 104 (1963)

    Article  ADS  Google Scholar 

  38. I.O. Kulik, A.N. Omel’yanchuk, Fiz. Nizk. Temp. 4, 296 (1978) [Sov. J. Low Temp. Phys. 4, 142 (1978)]

    ADS  Google Scholar 

  39. H. Arie, K. Yasuda, H. Kobayashi, I. Iguchi, Y. Tanaka, S. Kashiwaya, Phys. Rev. B 62, 11864 (2000)

    Article  ADS  Google Scholar 

  40. J.J.A. Baselmans, T.T. Heikkilä, B.J. van Wees, T.M. Klapwijk, Phys. Rev. Lett. 89, 207002 (2002)

    Article  ADS  Google Scholar 

  41. It is well-known that using the BdG formalism for the spin up and down sectors constitutes double-counting [32]. Thus, the total energy and current are obtained by adding the contributions of the spin up and down sectors and dividing the result by two

  42. T. Löfwander, G. Johansson, M. Hurd, G. Wendin, Phys. Rev. B 57, R3225 (1998); M. Hurd, T. Löfwander, G. Johansson, G. Wendin, Phys. Rev. B 59, 4412 (1999)

    Google Scholar 

  43. Y. Tanaka, Phys. Rev. Lett. 72, 3871 (1994)

    Article  ADS  Google Scholar 

  44. A.M. Zagoskin, J. Phys.: Condens. Matter 9, L419 (1997)

  45. A. Huck, A. van Otterlo, M. Sigrist, Phys. Rev. B 56, 14163 (1997)

    Article  ADS  Google Scholar 

  46. M.H.S. Amin, S.N. Rashkeev, M. Coury, A.N. Omelyanchouk, A.M. Zagoskin, Phys. Rev. B 66, 174515 (2002)

    Article  ADS  Google Scholar 

  47. T. Lindström, S.A. Charlebois, A.Ya. Tzalenchuk, Z. Ivanov, M.H.S. Amin, A.M. Zagoskin, Phys. Rev. Lett. 90, 117002 (2003)

    Article  ADS  Google Scholar 

  48. I.K. Yanson, V.M. Svistunov, I.M. Dmitrenko, Zh. Eksp. Teor. Fiz. 48, 976 (1965) [Sov. Phys. JETP 21, 650 (1965)]

    Google Scholar 

  49. I.M. Dmitrenko, I.K. Yanson, JETP Lett. 2, 154 (1965)

    ADS  Google Scholar 

  50. D.N. Langenberg, D.J. Scalapino, B.N. Taylor, R.E. Eck, Phys. Rev. Lett. 15, 294 (1965)

    Article  ADS  Google Scholar 

  51. I.M. Dmitrenko, I.K. Yanson, I.I. Yurchenko, Fiz. Tverd. Tela 9, 3656 (1967) [Sov. Phys. Solid State 9, 2889 (1968)]

    Google Scholar 

  52. A.K. Jain, K.K. Likharev, J.E. Lukens, J.E. Savageau, Phys. Repts. 109, 309 (1984)

    Article  ADS  Google Scholar 

  53. R. Kleiner, F. Steinmeyer, G. Kunkel, P. Müller, Phys. Rev. Lett. 68, 2394 (1992)

    Article  ADS  Google Scholar 

  54. R.F. Miracky, J. Clarke, R.H. Koch, Phys. Rev. Lett. 50, 856 (1983)

    Article  ADS  Google Scholar 

  55. C.B. Whan, C.J. Lobb, M.G. Forrester, J. Appl. Phys. 77, 382 (1995)

    Article  ADS  Google Scholar 

  56. S. Shapiro, Phys. Rev. Lett. 11, 80 (1963); S. Shapiro, A.R. Janus, S. Holly, Rev. Mod. Phys. 36, 223 (1964)

    Article  ADS  Google Scholar 

  57. E.A. Early, A.F. Clark, K. Char, Appl. Phys. Lett. 62, 3357 (1993)

    Article  ADS  Google Scholar 

  58. L.C. Ku, H.M. Cho, J.H. Lu, S.Y. Wang, W.B. Jian, H.C. Yang, H.E. Horng, Physica C 229, 320 (1994)

    Article  ADS  Google Scholar 

  59. I.V. Borisenko, P.B. Mozhaev, G.A. Ovsyannikov, K.Y. Constantinian, E.A. Stepantsov, Physica C 368, 328 (2002)

    Article  ADS  Google Scholar 

  60. J. Clarke, Phys. Rev. Lett. 21, 1566 (1968)

    Article  ADS  Google Scholar 

  61. E. Il’ichev, M. Grajcar, R. Hlubina, R.P.J. Ijsselsteijn, H.E. Hoenig, H.-G. Meyer, A. Golubov, M.H.S. Amin, A.M. Zagoskin, A.N. Omelyanchouk, M.Yu. Kupriyanov, Phys. Rev. Lett. 86, 5369 (2001)

    Article  ADS  Google Scholar 

  62. D.J. Thouless, Phys. Rev. B 40, 12034 (1989)

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Department of Physics, University of Maryland, College Park, 20742-4111, Maryland, USA

    H.-J. Kwon & V. M. Yakovenko

  2. Department of Physics, Yale University, 06520-8120, New Haven, Connecticut, USA

    K. Sengupta

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  1. H.-J. Kwon
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  2. K. Sengupta
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  3. V. M. Yakovenko
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Correspondence to V. M. Yakovenko.

Additional information

Received: 24 September 2003, Published online: 2 April 2004

PACS:

74.50. + r Tunneling phenomena; point contacts, weak links, Josephson effects - 74.70.Kn Organic superconductors - 74.72.-h Cuprate superconductors (high-T c and insulating parent compounds) - 74.70.Pq Ruthenates

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Kwon, HJ., Sengupta, K. & Yakovenko, V.M. Fractional ac Josephson effect in p- and d-wave superconductors. Eur. Phys. J. B 37, 349–361 (2004). https://doi.org/10.1140/epjb/e2004-00066-4

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