Electronic and Thermal Sequential Transport in Metallic and Superconducting Two-Junction Arrays

Chapter
Part of the Engineering Materials book series (ENG.MAT.)

Abstract

The description of transport phenomena in devices consisting of arrays of tunnel junctions, and the experimental confirmation of these predictions is one of the great successes of mesoscopic physics. The aim of this paper is to give a self-consistent review of sequential transport processes in such devices, based on the so-called “orthodox” model. We calculate numerically the current-voltage (IV) curves, the conductance versus bias voltage (GV) curves, and the associated thermal transport in symmetric and asymmetric two-junction arrays such as Coulomb-blockade thermometers (CBTs), superconducting-insulator-normal-insulator-superconducting (SINIS) structures, and superconducting single-electron transistors (SETs). We investigate the behavior of these systems at the singularity-matching bias points, the dependence of microrefrigeration effects on the charging energy of the island, and the effect of a finite superconducting gap on Coulomb-blockade thermometry.

Referneces

  1. 1.
    D.V. Averin, K.K. Likharev, J. Low Temp. Phys. 62, 345 (1986); T.A. Fulton, G.J. Dolan, Phys. Rev. Lett. 59, 109 (1987)CrossRefGoogle Scholar
  2. 2.
    R.J. Schoelkopf, P. Wahlgren, A.A. Kozhevnikov, P. Delsing, D.E. Prober, Science 280, 1238 (1998); M.A. Sillanpä, L. Roschier, P.J. Hakonen, Phys. Rev. Lett. 93, 066805 (2004)CrossRefGoogle Scholar
  3. 3.
    M.H. Devoret, R.J. Schoelkopf, Nature 406, 1039 (2000)CrossRefGoogle Scholar
  4. 4.
    Y. Nakamura, Y.A. Pashkin, J.S. Tsai, Nature, 398, 786 (1999); Yu. Makhlin, G. Schön, A. Shnirman, Rev. Mod. Phys. 73, 357 (2001); D. Vion et. al., Science 296, 886 (2002); Y. Nakamura, Yu. A. Paskin, T. Yamamoto, J.S. Tsai, Phys. Rev. Lett. 88, 047901 (2002); Yu. A. Paskin et. al., Nature 421, 823 (2003); T. Yamamoto et. al., Nature 425, 941 (2003); T. Duty, D. Gunnarsson, K. Bladh, P. Delsing, Phys. Rev. B 69 132504 (2004); J.Q. You F. Nori, Physics Today 58, 42 (2005); G.S. Paraoanu, Phys. Rev. B 74, 140504(R) (2006). G.S. Paraoanu, Phys. Rev. Lett. 97, 180406 (2006); J. Li, K. Chalapat, G.S. Paraoanu, Phys. Rev. B 78, 064503 (2008); J. Li G.S. Paraoanu, New J. Phys. 11, 113020 (2009)Google Scholar
  5. 5.
    G.S. Paraoanu, A.M. Halvari, Appl. Phys. Lett. 86, 093101 (2005); T.F. Li et. al., Appl. Phys. Lett. 91, 033107 (2007)CrossRefGoogle Scholar
  6. 6.
    J.P. Pekola, K.P. Hirvi, J.P. Kauppinen, M.A. Paalanen, Phys. Rev. Lett. 73, 2903 (1994); K.P. Hirvi, J.P. Kauppinen, A.N. Korotkov, M.A. Paalanen, J.P. Pekola, Appl. Phys. Lett. 67, 2096 (1995); J.P. Kauppinen and J.P. Pekola, Phys. Rev. Lett. 77, 3889 (1996); Sh. Farhangfar, K.P. Hirvi, J.P. Kauppinen, J.P. Pekola, J.J. Toppari, D.V. Averin, A.N. Korotkov, J. Low Temp. Phys. 108, 191 (1997); J.P. Pekola, J.J. Toppari, J.P. Kauppinen, K.M. Kinnunen, A.J. Manninen, A.G.M. Jansen, J. Appl. Phys. 83, 5582 (1998); J.P. Kauppinen, K.T. Loberg, A.J. Manninen, J.P. Pekola, R.V. Voutilainen, Rev. Sci. Instrum. 69, 4166 (1998)CrossRefGoogle Scholar
  7. 7.
    M.M. Leivo, J.P. Pekola, D.V. Averin, Appl. Phys. Lett. 68, 1996 (1996); J.P. Pekola, F. Giazotto, O.-P. Saira, Phys. Rev. Lett. 98, 037201 (2007); O.-P. Saira, M. Meschke, F. Giazotto, A.M. Savin, M. Mottonen, J.P. Pekola, Phys. Rev. Lett. 99, 027203 (2007)CrossRefGoogle Scholar
  8. 8.
    A.B. Zorin, S.V. Lotkhov, H. Zangerle, J. Niemeyer, J. Appl. Phys. 88, 2665 (2000); R. Dolata, H. Scherer, A.B. Zorin, V.A. Krupenin, J. Niemyer, Appl. Phys. Lett. 80 2776 (2002); N. Kim et. al., Physica B 329–333, 1519 (2003); G.S. Paraoanu, A. Halvari, Rev. Adv. Mater. Sci. 5, 265 (2003); M. Watanabe, Y. Nakamura, J.-S. Tsai, Appl. Phys. Lett. 84 410 (2004); A.M. Savin et. al., Appl. Phys. Lett. 91, 063512 (2007)CrossRefGoogle Scholar
  9. 9.
    J. Bardeen, Phys. Rev. Lett. 6 57 (1961)CrossRefGoogle Scholar
  10. 10.
    F. Giazotto, T.T. Heikkilä, A. Luukanen, A.M. Savin, J. Pekola, Rev. Mod. Phys. 78, 217 (2006)CrossRefGoogle Scholar
  11. 11.
    G.-L. Ingold, Yu.V. Nazarov, “Charge tunneling rates in ultrasmall junctions”, in Single Charge Tunneling, edited by H. Grabert, M.H. Devoret (Plenum, New York, NY 1992), pp. 21–108Google Scholar
  12. 12.
    G. Schön, “Single-electron tunneling”, in T. Dittrich, P. Hänggi, G. Ingold, B. Kramer, G. Schön, W. Zwerger, Quantum Transport and Dissipation (VCH Verlag 1997), Chapter 3.
  13. 13.
    W.A. Harrison, Phys. Rev. 123, 85 (1961).CrossRefGoogle Scholar
  14. 14.
    J.G. Simons, J. Appl. Phys. 34, 1793 (1963); T.E. Hartman, J. Appl. Phys. 35, 3283 (1964); W.F. Brinkman, R.C. Dynes, J.M. Rowell, J. Appl. Phys. 41, 1915 (1970);CrossRefGoogle Scholar
  15. 15.
    W.A. Hofer, A.S. Foster, A.S. Shluger Rev. Mod. Phys. 75, 1287 (2003)CrossRefGoogle Scholar
  16. 16.
    P. Törmä, P. Zoller, Phys. Rev. Lett. 85, 487 (2000); Gh.-S. Paraoanu, M. Rodriguez, P. Törmä, J. Phys. B. 34, 4763 (2001); Gh.-S. Paraoanu, M. Rodriguez, P. Törmä, Phys. Rev. A 66, 041603 (2002); J. Kinnunen, M. Rodriguez, P. Törmä, Science 305, 1131 (2004).CrossRefGoogle Scholar
  17. 17.
    R.C. Dynes et. al., Phys. Rev. Lett. 53, 2437 (1984); M. Kunchur et. al., Phys. Rev. B 36, 4062 (1987); J.P. Pekola et. al., Phys. Rev. Lett. 92, 056804 (2004)CrossRefGoogle Scholar
  18. 18.
    J.J. Toppari, T. Kühn, A. P. Halvari, J. Kinnunen, M. Leskinen, G.S. Paraoanu, Phys. Rev. B 76, 172505 (2007)CrossRefGoogle Scholar
  19. 19.
    J.J. Toppari, T. Kühn, A.M. Halvari, G.S. Paraoanu, J. Phys.: Conf. Ser. 150, 022088 (2009)CrossRefGoogle Scholar
  20. 20.
    Y.T. Tan, T. Kamiya, Z.A.K. Durrani, H. Ahmed, J. Appl. Phys. 94, 633 (2003); K. Luo, D.-H. Chae1, Z. Yao, Nanotechnol. 18 465203 (2007)CrossRefGoogle Scholar
  21. 21.
    H. van Houten, C.W.J. Beenakker, A.A.M. Staring, “Coulomb-blockade oscillations in semiconductor nanostructures”, in Single Charge Tunneling, ed by H. Grabert, M.H. Devoret (Plenum, New York, 1992), pp. 167–216Google Scholar
  22. 22.
    S. Kafanov, A. Kemppinen, Yu. A. Pashkin, M. Meschke, J.S. Tsai, J.P. Pekola , Phys. Rev. Lett. 103, 120801 (2009)CrossRefGoogle Scholar
  23. 23.
    D.V. Averin and K.K. Likharev, “Single electronics: a correlated transfer of single electrons and Cooper pairs in systems of small tunnel junctions”, in B.L. Altshuler. P.A. Lee, R.A. Webb, Mesoscopic phenomena in solids, (Elsevier Science, New York, NY, 1991)Google Scholar
  24. 24.
    P.J. Koppinen, T. Kühn, I.J. Maasilta, J. Low. Temp. Phys. 154, 179 (2009)CrossRefGoogle Scholar
  25. 25.
    J.P. Pekola, J.J. Vartiainen, M. Möttönen, O.-P. Saira, M. Meschke, D.V. Averin, Nature Phys. 4, 120 (2008)CrossRefGoogle Scholar
  26. 26.
    A.N. Korotkov, Appl. Phys. Lett. 69 2593 (1996)CrossRefGoogle Scholar
  27. 27.
    Y. Nakamura, A.N. Korotkov, C.D. Chen, J.S. Tsai, Phys. Reb. B 56, 5116 (1997)CrossRefGoogle Scholar
  28. 28.
    A.J. Manninen, Yu. A. Pashkin, A.N. Korotkov, J.P. Pekola, Europhys. Lett. 39, 305 (1997)CrossRefGoogle Scholar
  29. 29.
    M.G. Blamire, E.C.G. Kirk, J.E. Evetts, T.M. Klapwijk, Phys. Rev. Lett. 66, 220 (1991)CrossRefGoogle Scholar
  30. 30.
    A.J. Manninen, J.K. Suoknuuti, M.M. Leivo, J.P. Pekola, Apl. Phys. Lett. 74 3020 (1999)CrossRefGoogle Scholar

Copyright information

© Springer –Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.NanoScience Center and Department of PhysicsUniversity of JyväskyläJyväskyläFinland
  2. 2.Low Temperature LaboratorySchool of Science and Technology, Aalto UniversityAALTOFinland

Personalised recommendations