Skip to main content
SpringerLink
Log in

Thermoelectric effects in superconducting proximity structures

  • Published:
Applied Physics A Aims and scope Submit manuscript

Abstract

Attaching a superconductor in good contact with a normal metal gives rise to a proximity effect where the superconducting correlations leak into the normal metal. An additional contact close to the first one makes it possible to carry a supercurrent through the metal. Forcing this supercurrent flow along with an additional quasiparticle current from one or many normal-metal reservoirs leads many interesting effects. The supercurrent can be used to tune the local energy distribution function of the electrons. This mechanism also leads to finite thermoelectric effects even in the presence of electron–hole symmetry. Here we review these effects and discuss to which extent the existing observations of thermoelectric effects in metallic samples can be explained through the use of the dirty limit quasiclassical theory.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. K.D. Usadel, Phys. Rev. Lett. 25, 507 (1970)

    Article  ADS  Google Scholar 

  2. W. Belzig, F.K. Wilhelm, C. Bruder, G. Schön, A.D. Zaikin, Superlattices Microstruct. 25, 1251 (1999)

    Article  ADS  Google Scholar 

  3. V. Chandrasekhar, in The Physics of Superconductors, vol. II, ed. by K.H. Bennemann, J.B. Ketterson (Springer, Berlin, Heidelberg, New York, 2004)

  4. V.T. Petrashov, K.G. Chua, K.M. Marshall, R.S. Shaikhaidarov, J.T. Nicholls, Phys. Rev. Lett. 95, 147001 (2005)

    Article  ADS  Google Scholar 

  5. M. Cutler, N.F. Mott, Phys. Rev. 181, 1336 (1969)

    Article  ADS  Google Scholar 

  6. L. Onsager, Phys. Rev. 37, 405 (1931)

    Article  MATH  ADS  Google Scholar 

  7. H.B.G. Casimir, Rev. Mod. Phys. 17, 343 (1945)

    Article  ADS  Google Scholar 

  8. H.B. Callen, Phys. Rev. 73, 1349 (1948)

    Article  MATH  ADS  Google Scholar 

  9. N.R. Claughton, C.J. Lambert, Phys. Rev. B 53, 6605 (1996)

    Article  ADS  Google Scholar 

  10. A.F. Andreev, Sov. Phys. J. Exp. Theor. Phys. 19, 1228 (1964)

    Google Scholar 

  11. T.T. Heikkilä, M.P. Stenberg, M.M. Salomaa, C.J. Lambert, Physica B 284–288, 1862 (2000)

  12. Y.M. Galperin, V.L. Gurevich, V.I. Kozub, A.L. Shelankov, Phys. Rev. B 65, 64531 (2002)

    Article  ADS  Google Scholar 

  13. A. Schmid, G. Schön, Phys. Rev. Lett. 43, 793 (1979)

    Article  ADS  Google Scholar 

  14. F. Giazotto, T.T. Heikkilä, A. Luukanen, A. Savin, J. Pekola, Rev. Mod. Phys. 78, 217 (2006)

    Article  ADS  Google Scholar 

  15. R. Seviour, A.F. Volkov, Phys. Rev. B 62, 6116 (2000)

    Article  ADS  Google Scholar 

  16. V.R. Kogan, V.V. Pavlovskii, A.F. Volkov, Europhys. Lett. 59, 875 (2002)

    Article  ADS  Google Scholar 

  17. P. Virtanen, T.T. Heikkilä, Phys. Rev. Lett. 92, 177004 (2004)

    Article  ADS  Google Scholar 

  18. P. Virtanen, T.T. Heikkilä, J. Low Temp. Phys. 136, 401 (2004)

    Article  Google Scholar 

  19. A.F. Volkov, V.V. Pavlovskii, Phys. Rev. B 72, 14529 (2005)

    Article  ADS  Google Scholar 

  20. P. Virtanen, T.T. Heikkilä, Phys. Rev. B 75, 104517 (2007)

    Article  ADS  Google Scholar 

  21. N.B. Kopnin, Theory of Nonequilibrium Superconductivity, in International Series of Monographs on Physics (Oxford University Press, Oxford, 2001), no. 110

  22. A. Schmid, G. Schön, J. Low Temp. Phys. 20, 207 (1975)

    Google Scholar 

  23. A.V. Zaitsev, Sov. Phys. J. Exp. Theor. Phys. 59, 1015 (1984)

    Google Scholar 

  24. Y.V. Nazarov, Superlattices Microstruct. 25, 1221 (1999)

    Article  ADS  Google Scholar 

  25. K.K. Likharev, Rev. Mod. Phys. 51, 101 (1979)

    Article  ADS  Google Scholar 

  26. M. Tinkham, Introduction to Superconductivity (McGraw-Hill, New York, 1996), 2nd edn.

  27. A.F. Andreev, Sov. Phys. J. Exp. Theor. Phys. 22, 455 (1966)

    Google Scholar 

  28. I.O. Kulik, Sov. Phys. J. Exp. Theor. Phys. 30, 944 (1970)

    Google Scholar 

  29. N.B. Kopnin, A.S. Mel’nikov, V.M. Vinokur, Phys. Rev. Lett. 96, 146802 (2006)

    Article  ADS  Google Scholar 

  30. F.K. Wilhelm, G. Schön, A.D. Zaikin, Phys. Rev. Lett. 81, 1682 (1998)

    Article  ADS  Google Scholar 

  31. T.T. Heikkilä, J. Särkkä, F.K. Wilhelm, Phys. Rev. B 66, 184513 (2002)

    Article  ADS  Google Scholar 

  32. B.J. van Wees, K.-M.H. Lenssen, C.J.P.M. Harmans, Phys. Rev. B 44, 470 (1991)

    Article  ADS  Google Scholar 

  33. S.-K. Yip, Phys. Rev. B 58, 5803 (1998)

    Article  ADS  Google Scholar 

  34. A.F. Volkov, Phys. Rev. Lett. 74, 4730 (1995)

    Article  ADS  Google Scholar 

  35. J.J.A. Baselmans, A.F. Morpurgo, B.J. van Wees, T.M. Klapwijk, Nature 397, 43 (1999)

    Article  ADS  Google Scholar 

  36. J.J.A. Baselmans, B.J. van Wees, T.M. Klapwijk, Phys. Rev. B 63, 094504 (2001)

    Article  ADS  Google Scholar 

  37. J. Huang, F. Pierre, T.T. Heikkilä, F.K. Wilhelm, N.O. Birge, Phys. Rev. B 66, 020507 (2002)

    Article  ADS  Google Scholar 

  38. T. Schäpers, J. Malindretos, K. Neurohr, S. Lachenmann, A. van der Hart, G. Crecelius, H. Hartdegen, H. Lüth, A.A. Golubov, Appl. Phys. Lett. 73, 2348 (1998)

    Article  ADS  Google Scholar 

  39. J. Kutchinsky, R. Taboryski, C.B. Sorensen, J. Bindslev Hansen, P.E. Lindelof, Phys. Rev. Lett. 83, 4856 (1999)

    Article  ADS  Google Scholar 

  40. R. Shaikhaidarov, A.F. Volkov, H. Takayanagi, V.T. Petrashov, P. Delsing, Phys. Rev. B 62, R14649 (2000)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  42. M.S. Crosser, P. Virtanen, T.T. Heikkilä, N.O. Birge, Phys. Rev. Lett. 96, 167004 (2006)

    Article  ADS  Google Scholar 

  43. T.T. Heikkilä, T. Vänskä, F.K. Wilhelm, Phys. Rev. B 67, 100502(R) (2003)

  44. T.T. Heikkilä, Superconducting Proximity Effect in Mesoscopic Metals, Ph.D. thesis, Helsinki University of Technology (2002)

  45. A.F. Volkov, A.V. Zaitsev, Phys. Rev. B 53, 9267 (1996)

    Article  ADS  Google Scholar 

  46. H. Courtois, P. Charlat, P. Gandit, D. Mailly, B. Pannetier, J. Low Temp. Phys. 116, 187 (1999)

    Article  Google Scholar 

  47. S.G. den Hartog, C.M.A. Kapteyn, B.J. van Wees, T.M. Klapwijk, G. Borghs, Phys. Rev. Lett. 77, 4954 (1996)

    Article  ADS  Google Scholar 

  48. G.R. Boogaard, A.H. Verbruggen, W. Belzig, T.M. Klapwijk, Phys. Rev. B 69, 220503 (2004)

    Article  ADS  Google Scholar 

  49. H. Pothier, S. Guéron, D. Esteve, M.H. Devoret, Phys. Rev. Lett. 73, 2488 (1994)

    Article  ADS  Google Scholar 

  50. P.G.N. de Vegvar, T.A. Fulton, W.H. Mallison, R.E. Miller, Phys. Rev. Lett. 73, 1416 (1994)

    Article  ADS  Google Scholar 

  51. V.T. Petrashov, V.N. Antonov, P. Delsing, T. Claeson, Phys. Rev. Lett. 74, 5268 (1995)

    Article  ADS  Google Scholar 

  52. P. Charlat, H. Courtois, P. Gandit, D. Mailly, A.F. Volkov, B. Pannetier, Phys. Rev. Lett. 77, 4950 (1996)

    Article  ADS  Google Scholar 

  53. H. Courtois, P. Gandit, D. Mailly, B. Pannetier, Phys. Rev. Lett. 76, 130 (1996)

    Article  ADS  Google Scholar 

  54. W. Belzig, R. Shaikhaidarov, V.V. Petrashov, Y.V. Nazarov, Phys. Rev. B 66, 220505 (2002)

    Article  ADS  Google Scholar 

  55. Y.V. Nazarov, T.H. Stoof, Phys. Rev. Lett. 76, 823 (1996)

    Article  ADS  Google Scholar 

  56. T.H. Stoof, Y.V. Nazarov, Phys. Rev. B 53, 14496 (1996)

    Article  ADS  Google Scholar 

  57. A.A. Golubov, F.K. Wilhelm, A.D. Zaikin, Phys. Rev. B 55, 1123 (1997)

    Article  ADS  Google Scholar 

  58. C.J. Lambert, R. Raimondi, J. Phys. C Condens. Matter 10, 901 (1998)

    Article  ADS  Google Scholar 

  59. E. Zhao, T. Löfwander, J.A. Sauls, Phys. Rev. Lett. 91, 077003 (2003)

    Article  ADS  Google Scholar 

  60. E.V. Bezuglyi, V. Vinokur, Phys. Rev. Lett. 91, 137002 (2003)

    Article  ADS  Google Scholar 

  61. Z. Jiang, V. Chandrasekhar, Phys. Rev. Lett. 94, 147002 (2005)

    Article  ADS  Google Scholar 

  62. Z. Jiang, V. Chandrasekhar, Phys. Rev. B 72, 020502 (2005)

    Article  ADS  Google Scholar 

  63. D.A. Dikin, S. Jung, V. Chandrasekhar, Phys. Rev. B 65, 12511 (2002)

    Article  ADS  Google Scholar 

  64. D.A. Dikin, S. Jung, V. Chandrasekhar, Europhys. Lett. 57, 564 (2002)

    Article  ADS  Google Scholar 

  65. J. Eom, C.-J. Chien, V. Chandrasekhar, Phys. Rev. Lett. 81, 437 (1998)

    Article  ADS  Google Scholar 

  66. Z. Jiang, V. Chandrasekhar, Chin. J. Phys. 43, 693 (2005)

    Google Scholar 

  67. A. Parsons, I.A. Sosnin, V.T. Petrashov, Phys. Rev. B 67, 140502 (2003)

    Article  ADS  Google Scholar 

  68. A. Parsons, I.A. Sosnin, V.T. Petrashov, Physica E 18, 316 (2003)

    Article  ADS  Google Scholar 

  69. J. Zou, I. Sosnin, P. Virtanen, M. Meschke, V.T. Petrashov, T.T. Heikkilä, J. Low Temp. Phys. 146, 193 (2007)

    Article  ADS  Google Scholar 

  70. M. Meschke, W. Guichard, J. Pekola, Nature 444, 187 (2006)

    Article  ADS  Google Scholar 

  71. T.T. Heikkilä, F.K. Wilhelm, G. Schön, Europhys. Lett. 51, 434 (2000)

    Article  ADS  Google Scholar 

  72. C.J. Pethick, H. Smith, Phys. Rev. Lett. 43, 640 (1979)

    Article  ADS  Google Scholar 

  73. J. Clarke, B.R. Fjordbøge, P.E. Lindelof, Phys. Rev. Lett. 43, 642 (1979)

    Article  ADS  Google Scholar 

  74. J. Clarke, M. Tinkham, Phys. Rev. Lett. 44, 106 (1980)

    Article  ADS  Google Scholar 

  75. G. Srivastava, I. Sosnin, V.T. Petrashov, Phys. Rev. B 72, 012514 (2005)

    Article  ADS  Google Scholar 

  76. V.L. Ginzburg, Rev. Mod. Phys. 76, 981 (2004)

    Article  ADS  Google Scholar 

  77. G. Eilenberger, Z. Phys. 214, 195 (1968)

    Article  Google Scholar 

  78. T. Löfwander, M. Fogelström, Phys. Rev. B 70, 024515 (2004)

    Article  ADS  Google Scholar 

  79. F.K. Wilhelm, Ladungstransport in supraleitenden Nanostrukturen, Ph.D. thesis, University of Karlsruhe, Germany (1999)

  80. B. Meyer, Thermoelektrische Effekte in mesoskopischen Normal-/Supraleiter Heterostrukturen, Master’s thesis, University of Karlsruhe, Germany (1999)

  81. P. Samuelsson, H. Schomerus, Phys. Rev. B 63, 054512 (2001)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Low Temperature Laboratory, Helsinki University of Technology, P.O. Box 3500, 02015, Helsinki, Finland

    P. Virtanen & T.T. Heikkilä

Authors
  1. P. Virtanen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. T.T. Heikkilä
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to T.T. Heikkilä.

Additional information

PACS

74.25.Fy; 73.23.-b; 74.45.+c; 74.40.+k

Rights and permissions

Reprints and permissions

About this article

Cite this article

Virtanen, P., Heikkilä, T. Thermoelectric effects in superconducting proximity structures. Appl. Phys. A 89, 625–637 (2007). https://doi.org/10.1007/s00339-007-4189-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00339-007-4189-0

Keywords

Search

Navigation