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Magnetic Field Effects in Josephson Junctions

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Book cover Fundamentals and Frontiers of the Josephson Effect

Part of the book series: Springer Series in Materials Science ((SSMATERIALS,volume 286))

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Abstract

The chapter starts by describing Meissner screening and flux focusing in planar and nearly planar geometries, important for device applications. It then treats the Josephson effect in static magnetic fields through the Sine-Gordon equation, including magnetic interference patterns for single junctions and dc SQUIDs, in both the conventional case and the case with intrinsic phase shifts. These intrinsic phase shifts can occur either in the junction, along the junction, or in the electrodes connecting junctions. There is a discussion of integer, half-integer, and fractional Josephson vortices. Finally there is a discussion of time-dependent effects, including Fiske steps, zero field steps, and Josephson vortex propagation.

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References

  1. H. Bluhm, Magnetic fields above the surface of a superconductor with internal magnetism. Phys. Rev. B 76, 144507 (2007)

    Article  ADS  Google Scholar 

  2. W.H. Chang, Numerical calculation of the inductances of a multi-superconductor transmission line system. IEEE Trans. Magn. MAG-17(1), 764–766 (1981)

    Article  ADS  Google Scholar 

  3. E.H. Brandt, Thin superconductors and SQUIDs in perpendicular magnetic field. Phys. Rev. B 72, 024529 (2005)

    Article  ADS  Google Scholar 

  4. M. Kamon, M.J. Tsuk, J.K. White, FASTHENRY: a multipole-accelerated 3-D inductance extraction program. IEEE Trans. Microw. Theory Techn. 42, 1750–1758 (1994)

    Article  ADS  Google Scholar 

  5. E.H. Brandt, J.R. Clem, Superconducting thin rings with finite penetration depth. Phys. Rev. B 69, 184509 (2004)

    Article  ADS  Google Scholar 

  6. M.B. Ketchen, W.J. Gallagher, A.W. Kleinsasser, S. Murphy, J.R. Clem, DC SQUID flux focuser, in SQUID’85–Superconducting Quantum Interference Devices and their Applications (Walter de Gruyter and Co., Berlin, New York, 1985), pp. 865–871

    Google Scholar 

  7. A. Barone, G. Paterno, Physics and Applications of the Josephson Effect (Wiley, New York, 1982), p. 2

    Book  Google Scholar 

  8. L.N. Bulaevskii, V.V. Kuzii, A.A. Sobyanin, Superconducting system with weak coupling to current in ground-state. JETP Lett. 25, 290 (1977)

    ADS  Google Scholar 

  9. B.I. Spivak, S.A. Kivelson, Negative local superfluid densities: the difference between dirty superconductors and dirty Bose liquids. Phys. Rev. B 43, 3740–3743(R) (1991)

    Article  ADS  Google Scholar 

  10. V.B. Geshkenbein, A.I. Larkin, The Josephson effect in superconductors with heavy fermions. JETP Lett. 43, 395 (1986)

    ADS  Google Scholar 

  11. V.B. Geshkenbein, A.I. Larkin, A. Barone, Vortices with half magnetic-flux quanta in heavy-fermion superconductors. Phys. Rev. B 36, 235 (1987)

    Article  ADS  Google Scholar 

  12. M. Sigrist, T.M. Rice, Paramagnetic effect in high-\({\text{ T }}_c\) superconductors–a hint for d-wave superconductivity. J. Phys. Soc. Jpn. 61, 4283 (1992)

    Article  ADS  Google Scholar 

  13. M. Sigrist, T.M. Rice, Unusual paramagnetic phenomena in granular high-temperature superconductors–a consequence of \(d\)-wave pairing? Rev. Mod. Phys. 67, 503 (1995)

    Article  ADS  Google Scholar 

  14. A.V. Andreev, A.I. Buzdin, R.M. Osgood, \(\pi \) phase in magnetic-layered superconductors. Phys. Rev. B 43, 10124 (1991)

    Article  ADS  Google Scholar 

  15. V.V. Ryazanov, V.A. Obozonov, A.V. Veretennikov, A.Y. Rusanov, Intrinsically frustrated superconducting array of superconductor-ferromagnet-superconductor \(\pi \) junctions. Phys. Rev. B 65, 020501(R) (2001)

    Article  Google Scholar 

  16. A. Bauer, J. Bentner, M. Aprili, M.L. Della Rocca, M. Reinwald, W. Wegscheider, C. Strunk, Spontaneous supercurrent induced by ferromagnetic \(\pi \) junctions. Phys. Rev. Lett. 92, 217001 (2004)

    Google Scholar 

  17. J.J.A. Baselmans, A.F. Morpurgo, B.J. van Wees, T.M. Klapwijk, Reversing the direction of the super current in a controllable Josephson junction. Nature 397, 43–45 (1998)

    Article  ADS  Google Scholar 

  18. E. Goldobin, A. Sterck, T. Gaber, D. Koelle, R. Kleiner, Dynamics of semifluxons in Nb long Josephson \(0-\pi \) junctions. Phys. Rev. Lett. 92, 057005 (2004)

    Article  ADS  Google Scholar 

  19. E. Goldobin, D. Koelle, R. Kleiner, Ground states of one and two tractional vortices in long Josephson \(0-\kappa \) junctions. Phys. Rev. B 70, 174519 (2004)

    Article  ADS  Google Scholar 

  20. T. Gaber, E. Goldobin, A. Sterck, R. Kleiner, D. Koelle, M. Siegel, M. Neuhaus, Nonideal artifical phase discontinuity in long Josephson \(0-\kappa \) junctions. Phys. Rev. B 72, 054522 (2005)

    Article  ADS  Google Scholar 

  21. R.C. Dynes, T.A. Fulton, Supercurrent density distribution in Josephson junctions. Phys. Rev. B 3, 3015–3023 (1971)

    Article  ADS  Google Scholar 

  22. J. Matisoo, Critical currents and current distributions in Josephson junctions. J. Appl. Phys. 40, 1812–1820 (1969)

    ADS  Google Scholar 

  23. J.M. Rowell, Magnetic field dependence of the Josephson tunnel current. Phys. Rev. Lett. 11, 200–202 (1963)

    Article  ADS  Google Scholar 

  24. A. Barone, G. Paterno, M. Russo, R. Vaglio, Differentiation and interference phenomena in single Josephson junctions. Phys. Status Solidi(a) 41, 393–401 (1977)

    Google Scholar 

  25. S. Hart, H. Ren, T. Wagner, P. Leubner, M. Mühlbauer, C. Brüne, L.W. Molenkamp, A. Yacoby, Induced superconductivity in the quantum spin Hall edge. Nat. Phys. 10, 638–643 (2014)

    Article  Google Scholar 

  26. C.S. Owen, D.J. Scalapino, Vortex structure and critical currents in Josephson junctions. Phys. Rev. 164, 538–544 (1967)

    Article  ADS  Google Scholar 

  27. J.R. Kirtley, K.A. Moler, D.J. Scalapino, Spontaneous flux and magnetic-interference patterns in 0-\(\pi \) Josephson junctions. Phys. Rev. B 56, 886–891 (1997)

    Article  ADS  Google Scholar 

  28. J.R. Clem, M.W. Coffey, Viscous flux motion in a Josephson-coupled layer model of high-\(T_c\) superconductors. Phys. Rev. B 42, 6209–6216 (1990)

    Article  ADS  Google Scholar 

  29. J.H. Xu, J.H. Miller Jr., C.S. Ting, \(\pi \)-vortex state in a long \(0-\pi \) Josephson junction. Phys. Rev. B 51, 11958–11961 (1995)

    Article  ADS  Google Scholar 

  30. J.R. Kirtley, C.C. Tsuei, M. Rupp, J.Z. Sun, L.S. Yu-Jahnes, A. Gupta, M.B. Ketchen, K.A. Moler, M. Bhushan, Direct imaging of integer and half-integer Josephson vortices in high-\(T_c\) grain boundaries. Phys. Rev. Lett. 76, 1336–1339 (1996)

    Article  ADS  Google Scholar 

  31. D.A. Wollman, D.J. Van Harlingen, W.C. Lee, D.M. Ginsberg, A.J. Leggett, Experimental determination of the superconducting pairing state in YBCO from the phase coherence of YBCO-PB dc SQUIDs. Phys. Rev. Lett. 71, 2134–2137 (1993)

    Article  ADS  Google Scholar 

  32. D.A. Wollman, D.J. Van Harlingen, J. Giapintzakis, D.M. Ginsberg, Evidence for \(d_{x^{2}-y^{2}}\) pairing from the magnetic field modulation of YBa\(_2\)Cu\(_3\)O\(_7\)-Pb Josephson junctions. Phys. Rev. Lett. 74, 797–800 (1995)

    Article  ADS  Google Scholar 

  33. M.D. Fiske, Temperature and magnetic field dependence of the Josephson tunneling current. Rev. Mod. Phys. 36, 221–222 (1964)

    Article  ADS  Google Scholar 

  34. D.N. Langenberg, D.J. Scalapino, B.N. Taylor, R.E. Eck, Investigation of microwave radiation emitted by Josephson junctions. Phys. Rev. Lett. 15, 294–297 (1965)

    Article  ADS  Google Scholar 

  35. I.O. Kulik, Theory of “steps” of voltage-current characteristics of the Josephson tunnel current. Zh. Esker. Teor. Pis. Red. 2, 134(1965). JETP Lett. 2, 84–87 (1965)

    Google Scholar 

  36. R.E. Eck, D.J. Scalapino, B.N. Taylor, Self-detection of the ac Josephson current. Phys. Rev. Lett. 13, 15–18 (1964)

    Article  ADS  Google Scholar 

  37. I.O. Kulik, Theory of resonance phenomena in superconducting tunneling. Zh. Tekh. Fiz. 37, 157–166 (1967). Sov. Phys. Tech. Phys. 12, 111–116 (1967)

    Google Scholar 

  38. G. Paterno, J. Nordman, Self-resonant modes in Nb-NbO\(_x\)-Pb Josephson junctions. J. Appl. Phys. 49, 2456–2460 (1978)

    Article  ADS  Google Scholar 

  39. J.T. Chen, T.F. Finnegan, D.N. Langenberg, Anomalous d.c. current singularities in Josephson tunnel junctions. ICSS 413-420 (1969)

    Article  ADS  Google Scholar 

  40. P.S. Lomdahl, O.H. Sorensen, P.L. Christiansen, Soliton excitations in Josephson tunnel junctions. Phys. Rev. B 25, 5737–5748 (1982)

    Article  ADS  Google Scholar 

  41. T.A. Fulton, R.C. Dynes, Single vortex propagation in Josephson junctions. Solid State Commun. 12, 57–61 (1973)

    Article  ADS  Google Scholar 

  42. A. Davidson, B. Dueholm, B. Kryger, N.F. Pedersen, Experimental investigation of trapped sine-Gordon solitons. Phys. Rev. Lett. 55, 2059–2062 (1985)

    Article  ADS  Google Scholar 

  43. A.V. Ustinov, T. Doderer, R.P. Huebener, N.F. Pedersen, B. Mayer, V.A. Oboznov, Dynamics of sine-Gordon solitons in the annular Josephson junction. Phys. Rev. Lett. 69, 1815–1818 (1992)

    Article  ADS  Google Scholar 

  44. P. Binder, D. Abraimov, A.V. Ustinov, S. Flach, Y. Zolotaryuk, Observation of breathers in Josephson ladders. Phys. Rev. Lett. 84, 745–748 (2000)

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Stanford University, Palo Alto, CA, USA

    John R. Kirtley

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  1. John R. Kirtley
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Correspondence to John R. Kirtley .

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  1. Dipartimento di Fisica “E.Pancini”, Università di Napoli Federico II, Napoli, Italy

    Francesco Tafuri

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Kirtley, J.R. (2019). Magnetic Field Effects in Josephson Junctions. In: Tafuri, F. (eds) Fundamentals and Frontiers of the Josephson Effect. Springer Series in Materials Science, vol 286. Springer, Cham. https://doi.org/10.1007/978-3-030-20726-7_6

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