Skip to main content

Guided Vortex Motion and Vortex Ratchets in Nanostructured Superconductors

  • Chapter
  • First Online:
Nanoscience and Engineering in Superconductivity

Abstract

In type II superconductors, an external magnetic field can partially penetrate into the superconducting phase in the form of magnetic flux lines or vortices. The repulsive interaction between vortices makes them to arrange in a triangular lattice, known as Abrikosov vortex lattice. This periodic vortex distribution is very fragile and can be easily distorted by introducing pinning centers such as local alterations of the superconducting condensate density. The dominant role of the vortex-pinning site interaction not only permits to control the static vortex patterns and to enhance the maximum dissipationless current sustainable by the superconducting material but also allows one to gain control on the dynamics of vortices. Among the ultimate motivations behind the manipulation of the vortex motion are the better performance of superconductor-based devices by reducing the noise in superconducting quantum interference-based systems, development of superconducting terahertz emitters, reversible manipulation of local field distribution through flux lenses, or even providing a way to predefine the optical transmission through the system. In this chapter, we discuss two relevant mechanisms used in most envisaged fluxonics devices, namely the guidance of vortices through predefined paths and the rectification of the average vortex motion. The former can be achieved with any sort of confinement potential such as local depletion of the order parameter or local enhancements of the current density. In contrast, rectification effects result from the lack of inversion symmetry of the pinning landscape which tends to favor the vortex flow in one particular direction. We also discuss a new route for further flexibility and tunability of these fluxonics components by introducing ferromagnetic pinning centers interacting with vortices via their magnetic stray field.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. M. Vélez, J.I. Martín, J.E. Villegas, A. Hoffmann, E.M. Gonzalez, J.L. Vicent, Ivan K. Schuller, J. Magn. Magn. Mater. 320, 2547–62 (2008)

    Google Scholar 

  2. A. Aladyshkin, A.V. Silhanek, W. Gillijns, V.V. Moshchalkov, Supercond. Sci. Technol. 22, 053001 (2009)

    Article  ADS  Google Scholar 

  3. P. Reimann, Phys. Rep. 361, 57 (2002)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  4. P. Hänggi, F. Marchesoni, Rev. Mod. Phys. 81, 387 (2009)

    Article  ADS  Google Scholar 

  5. I. Giaever, Phys. Rev. Lett. 15, 825 (1966)

    Article  ADS  Google Scholar 

  6. E.H. Brandt, Phys. Rev. Lett. 50, 1599 (1983)

    Article  ADS  Google Scholar 

  7. E.H. Brandt, J. Low Temp. Phys. 53, 41 (1983)

    Article  ADS  Google Scholar 

  8. E.H. Brandt, J. Low Temp. Phys. 53, 71 (1983)

    Article  ADS  Google Scholar 

  9. D.X. Chen, J.J. Moreno, A. Hernando, A. Sanchez, B.Z. Li, Phys. Rev. B 57, 5059 (1998)

    Article  ADS  Google Scholar 

  10. C.P. Poole, H.A. Farach, R.J. Creswick, R. Prozorov, Superconductivity (Elsevier, London, 2007)

    Google Scholar 

  11. H. Suhl, Phys. Rev. Lett. 14, 226 (1965)

    Article  MathSciNet  ADS  Google Scholar 

  12. E. Simanek, Phys. Lett. A 154, 309 (1991)

    Article  ADS  Google Scholar 

  13. E.M. Chudnovsky, A.B. Kuklov, Phys. Rev. Lett. 91, 067004 (2003)

    Article  ADS  Google Scholar 

  14. A. van Otterlo, M. Feigel’man, V. Geshkenbein, G. Blatter, Phys. Rev. Lett. 75, 3736 (1995)

    Article  ADS  Google Scholar 

  15. N.B. Kopnin, V.M. Vinokur, Phys. Rev. Lett. 81, 3952 (1998)

    Article  ADS  Google Scholar 

  16. M.J. Stephen, J. Bardeen, Phys. Rev. Lett. 14, 112 (1965)

    Article  ADS  Google Scholar 

  17. J. Volger, F.A. Staas, A.G. van Vijfeijken, Phys. Lett. 9, 303 (1964)

    Article  ADS  Google Scholar 

  18. Y.B. Kim, C.F. Hempstead, A.R. Strnad, Phys. Rev. 16, A1163 (1965)

    Article  Google Scholar 

  19. M. Tinkham, Phys. Rev. Lett. 13, 804 (1964)

    Article  ADS  Google Scholar 

  20. J.R. Clem, Phys. Rev. Lett. 20, 735 (1968)

    Article  ADS  Google Scholar 

  21. M.A.R. LeBlanc, Supercond. Sci. Technol. 10, 929 (1997)

    Article  ADS  Google Scholar 

  22. J. Kolacek, P. Lipavsky, E.H. Brandt, Phys. Rev. Lett. 86, 312 (2001)

    Article  ADS  Google Scholar 

  23. P.G. de Gennes, J. Matricon, Rev. Mod. Phys. 36, 45 (1964)

    Article  ADS  Google Scholar 

  24. J. Bardeen, Phys. Rev. Lett. 13, 747 (1964)

    Article  ADS  Google Scholar 

  25. P. Ao, D.J. Thouless, Phys. Rev. Lett. 70, 2158 (1993)

    Article  ADS  Google Scholar 

  26. E.B. Sonin, Phys. Rev. Lett. 81, 4276 (1998)

    Article  ADS  Google Scholar 

  27. E.B. Sonin, Phys. Rev. B 55, 485 (1997)

    Article  ADS  Google Scholar 

  28. J. Pearl, Appl. Phys. Lett. 5, 65 (1964)

    Article  ADS  Google Scholar 

  29. H. Brandt, Phys. Rev. B 79, 134526 (2009)

    Article  MathSciNet  ADS  Google Scholar 

  30. A. Andronov, I. Gordion, V. Kurin, I. Nefedov, I. Shereshevsky, Physica C 213, 193 (1993)

    Article  ADS  Google Scholar 

  31. V.V. Moshchalkov, V. Bruyndoncx, L. Van Look, M.J. Van Bael, Y. Bruynseraede, A. Tonomura, Chapter 9 in Handbook of Nanostructured Materials and Nanotechnology, ed. by H.S. Nalwa, Electrical Properties, vol. 3 (Academic Press, New York, 2000)

    Google Scholar 

  32. J.I. Martín, J. Nogués, K. Liu, J.L. Vicent, I.K. Schuller, J. Magn. Magn. Mater. 256, 449 (2003)

    Article  ADS  Google Scholar 

  33. see for instance C. Reichhardt, C.J. Olson, S.B. Field, F. Nori, Phys. Rev. B 57, 7937 (1998)

    Google Scholar 

  34. see for instance K. Harada, O. Kamimura, H. Kasai, T. Matsuda, A. Tonomura, V.V. Moshchalkov, Science 274, 1167 (1996)

    Google Scholar 

  35. P. Vašek, I. Janeček, V. Plecháček, Physica C 247, 381 (1995)

    Article  ADS  Google Scholar 

  36. D. Jaque, E.M. Gonzalez, J.I. Martín, J.V. Anguita, J.L. Vicent, Appl. Phys. Lett. 81, 2851 (2002)

    Article  ADS  Google Scholar 

  37. A.I. Buzdin, Rev. Mod. Phys. 77, 935 (2005)

    Article  ADS  Google Scholar 

  38. A. Belkin, V. Novosad, M. Iavarone, J. Fedor, J.E. Pearson, A. Petrean-Troncalli, G. Karapetrov, Appl. Phys. Lett. 93, 072510 (2008)

    Article  ADS  Google Scholar 

  39. A. Belkin, V. Novosad, M. Iavarone, J. Pearson, G. Karapetrov, Phys. Rev. B 77, 180506 (2008)

    Article  ADS  Google Scholar 

  40. V. Vlasko-Vlasov, U. Welp, G. Karapetrov, V. Novosad, D. Rosenmann, M. Iavarone, A. Belkin, W-K. Kwok, Phys. Rev. B 77, 134518 (2008)

    Google Scholar 

  41. O. Daldini, C. Leemann, P. Martinoli, Solid State Comm. 16, 509 (1975)

    Article  ADS  Google Scholar 

  42. M. Baert, V.V. Metlushko, R. Jonckheere, V.V. Moshchalkov, Y. Bruynseraede, Phys. Rev. Lett. 74, 3269 (1995)

    Article  ADS  Google Scholar 

  43. F.A. Staas, A.K. Niessen, W.F. Druyvesteyn, J. Vonsuchtelen, Phys. Lett. 13, 293 (1964)

    Article  ADS  Google Scholar 

  44. A.K. Niessen, J. Vansuchtelen, F.A. Staas, W.F. Druyvesteyn, Philips Res. Rep. 20, 226 (1965)

    Google Scholar 

  45. A.K. Niessen, C.H. Weijsenfeld, J. Appl. Phys. 40, 384 (1969)

    Article  ADS  Google Scholar 

  46. Ya.V. Kopelevich, V.V. Lemanov, E.B. Sonin, A.L. Kholkin, JETP Lett. 50, 212 (1989)

    Google Scholar 

  47. T.L. Francavilla, R.A. Hein, IEEE Trans. Mag. 27, 1039 (1991)

    Article  ADS  Google Scholar 

  48. T.L. Francavilla, E.J. Cukauskas, L.H. Allen, P.R. Broussard, IEEE Trans. Appl. Supercond. 5, 1717 (1995)

    Article  Google Scholar 

  49. I.Yu. Antonova, V.M. Zakosarenko, E.V. II’ichev, V.I. Kuznetsov, V.A. Tullin, JETP Lett. 54, 505 (1991)

    ADS  Google Scholar 

  50. L.I. Glazman, Sov. J. Low Temp. Phys. 12, 389 (1986)

    Google Scholar 

  51. B. Chen, J. Dong, Phys. Rev. B 44, 10206 (1991)

    Article  ADS  Google Scholar 

  52. C. Villard, G. Koren, D. Cohen, E. Polturak, B. Thrane, D. Chateignier, Phys. Rev. Lett. 77, 3913 (1996)

    Article  ADS  Google Scholar 

  53. A.A. Prodan, V.A. Shklovskij, V.V. Chabanenko, A.V. Bondarenko, M.O. Obolenskii, H. Szymczak, S. Piechota, Physica C 302, 271 (1998)

    Article  ADS  Google Scholar 

  54. H. Pastoriza, S. Candia, G. Nieva, Phys. Rev. Lett. 83, 1026 (1999)

    Article  ADS  Google Scholar 

  55. V.V. Chabanenko, A.A. Prodan, V.A. Shklovskij, A.V. Bodarenko, M.A. Obolenskii, H. Szymczak, S. Piechota, Physica C 314, 133 (1999)

    Article  ADS  Google Scholar 

  56. G. D’Anna, V. Berseth, L. Forr’o, A. Erb, E. Walker, Phys. Rev. B 61, 10206 (2000)

    Article  ADS  Google Scholar 

  57. Y. Mawatari, Phys. Rev. B 56, 3433 (1997)

    Article  ADS  Google Scholar 

  58. Y. Mawatari, Phys. Rev. B 59, 12033 (1999)

    Article  ADS  Google Scholar 

  59. V.A. Shklovskii, A.K. Soroka, A.A. Soroka, JETP Lett. 89, 1138 (1999)

    Google Scholar 

  60. B.Y. Zhu, J. Dong, D.Y. Xing, Z.D. Wang, Phys. Rev. B 57, 5075 (1998)

    Article  ADS  Google Scholar 

  61. J. Groth, C. Reichhardt, C.J. Olson, et al., Phys. Rev. Lett. 77, 3625 (1996)

    Article  ADS  Google Scholar 

  62. G.W. Crabtree, G.K. Leaf, H.G. Kaper, V.M. Vinokur, A.E. Koshelev, D.W. Braun, D.M. Levine, W.K. Kwok, J.A. Fendrich, Physica C 263, 401 (1996)

    Article  ADS  Google Scholar 

  63. H. Ghamlouch, M. Aubin, Physica C 269, 163 (1996)

    Article  ADS  Google Scholar 

  64. O.K. Soroka, M. Huth, V.A. Shklovskij, J. Oster, H. Adrian, Physica C 388, 773 (2003)

    Article  ADS  Google Scholar 

  65. O.K. Soroka, V.A. Shklovskij, M. Huth, Phys. Rev. B 76, 014504 (2007)

    Article  ADS  Google Scholar 

  66. M.J. Hogg, F. Kahlmann, E.J. Tarte, Z.H. Barber, J.E. Evetts, Appl. Phys. Lett. 78, 1433 (2001)

    Article  ADS  Google Scholar 

  67. H. Pastoriza, P.H. Kes, Phys. Rev. Lett. 75, 3525 (1995)

    Article  ADS  Google Scholar 

  68. N. Kokubo, R. Besseling, V.M. Vinokur, P.H. Kes, Phys. Rev. Lett. 88, 247004 (2002)

    Article  ADS  Google Scholar 

  69. R. Besseling, N. Kokubo, P.H. Kes, Phys. Rev. Lett. 91, 177002 (2003)

    Article  ADS  Google Scholar 

  70. K. Yu, T.W. Heitmann, C. Song, M.P. DeFeo, B.L.T. Plourde, M.B.S. Hesselberth, P.H. Kes, Phys. Rev. B 76, 220507(R) (2007)

    Google Scholar 

  71. R. Wördenweber, P. Dymashevski, Physica C 404, 421 (2004)

    Article  ADS  Google Scholar 

  72. L. Van Look, B.Y. Zhu, R. Jonckheere, B.R. Zhao, Z.X. Zhao, V.V. Moshchalkov, Phys. Rev. B 66, 214511 (2002)

    Article  ADS  Google Scholar 

  73. M. Vélez, D. Jaque, J.I. Martín, M.I. Montero, I.K. Schuller, J.L. Vicent, Phys. Rev. B 65, 104511 (2002)

    Article  ADS  Google Scholar 

  74. J.E. Villegas, E.M. Gonzalez, M.I. Montero, I.K. Schuller, J.L. Vicent, Phys. Rev. B 68, 224504 (2003)

    Article  ADS  Google Scholar 

  75. C.E. Chialvo, J. Guimpel, S. Reparaz, H. Pastoriza, Physica C 422, 112 (2005)

    ADS  Google Scholar 

  76. C. Reichhardt, G. Zimanyi, N. Gronbech-Jensen, Phys. Rev. B 64, 014501 (2001)

    Article  ADS  Google Scholar 

  77. A.V. Silhanek, L. Van Look, S. Raedts, R. Jonkheere, V.V. Moshchalkov, Phys. Rev. B 68, 214504 (2003)

    Article  ADS  Google Scholar 

  78. J.E. Villegas, E.M. Gonzalez, M.I. Montero, I.K. Schuller, J.L. Vicent, Phys. Rev. B 72, 064507 (2005)

    Article  ADS  Google Scholar 

  79. C.C. de Souza Silva, G. Carneiro, Phys. Rev. B 66, 054514 (2002)

    Article  ADS  Google Scholar 

  80. G. Carneiro, Phys. Rev. B 66, 054523 (2002)

    Article  ADS  Google Scholar 

  81. V.A. Shklovskij, A.A. Soroka, Low Temp. Phys. 28, 254 (2002)

    Article  ADS  Google Scholar 

  82. R. Wördenweber, P. Dymashevski, V.R. Misko, Phys. Rev. B 69, 184504 (2004)

    Article  ADS  Google Scholar 

  83. R. Wördenweber, J.S.K. Sankarraj, P. Dymashevski, E. Hollmann, Physica C 434, 101 (2006)

    Article  ADS  Google Scholar 

  84. R. Wördenweber, E. Hollmann, J. Schubert, R. Kutzer, A.K. Ghosh, Appl. Phys. Lett. 94, 202501 (2009)

    Article  ADS  Google Scholar 

  85. M. Pannetier, R.J. Wijngaarden, I. Floan, J. Rector, B. Dam, R. Griessen, P. Lahl, R. Wördenweber, Phys. Rev. B 67, 212501 (2003)

    Article  ADS  Google Scholar 

  86. M. Menghini, R.J. Wijngaarden, A.V. Silhanek, S. Raedts, V.V. Moshchalkov, Phys. Rev. B 71, 104506 (2005)

    Article  ADS  Google Scholar 

  87. A. Lukashenko, A.V. Ustinov, A.P. Zhuravel, E. Hollmann, R. Wördenweber, J. Appl. Phys. 100, 023913 (2006)

    Article  ADS  Google Scholar 

  88. G. Carneiro, Physica C 432, 206 (2005)

    Article  ADS  Google Scholar 

  89. N. Verellen, A.V. Silhanek, W. Gillijns, V.V. Moshchalkov, V. Metlushko, F. Gozzini, B. Ilic Appl. Phys. Lett. 93, 022507 (2008)

    Article  ADS  Google Scholar 

  90. N. Verellen, A.V. Silhanek, W. Gillijns, V.V. Moshchalkov, V. Metlushko, F. Gozzini, B. Ilic, Appl. Phys. Lett. 94, 219903 (2009)

    Article  ADS  Google Scholar 

  91. A.V. Silhanek, J. Van de Vondel, A. Leo, G.W. Ataklti, W. Gillijns, V.V. Moshchalkov, Supercond. Sci. Technol. 22, 034002 (2009)

    Article  ADS  Google Scholar 

  92. J. Van de Vondel, A.V. Silhanek, V. Metlushko, P. Vavassori, B. Ilic, V.V. Moshchalkov, Phys. Rev. B 79, 054527 (2009)

    Article  ADS  Google Scholar 

  93. C.L.S. Lima, C.C. de Souza Silva, Phys. Rev. B 80, 054514 (2009)

    Article  ADS  Google Scholar 

  94. P. Hänggi, F. Marchesoni, F. Nori, Ann. Phys. (Leipz.) 14, 51–70 (2005)

    Article  MATH  ADS  Google Scholar 

  95. H. Linke, Appl. Phys. A 75 (special issue), 167 (2002)

    Google Scholar 

  96. J.H. Morais-Cabral, Y. Zhou, H. Mackinnon, Nature 414, 37 (2001)

    Article  ADS  Google Scholar 

  97. S. Matthias, F. Müller, Nature 424, 53 (2003)

    Article  ADS  Google Scholar 

  98. H. Linke, T.E. Humphrey, A. Löfgren, A.O. Sushkov, R. Newbury, R.P. Taylor, P. Omling, Science 286, 2314 (1999)

    Article  Google Scholar 

  99. C.-S. Lee, B. Jankó, I. Derényi, A.-L. Barabási, Nature 400, 337 (1999)

    Article  ADS  Google Scholar 

  100. J.F. Wambaugh, C. Reichhardt, C.J. Olson, F. Marchesoni, F. Nori, Phys. Rev. Lett. 83, 5106 (1999)

    Article  ADS  Google Scholar 

  101. B.Y. Zhu, F. Marchesoni, V.V. Moshchalkov, F. Nori, Phys. Rev. B 68, 014514 (2003)

    Article  ADS  Google Scholar 

  102. B.Y. Zhu, F. Marchesoni, F. Nori, Phys. Rev. Lett. 92, 180602 (2004)

    Article  ADS  Google Scholar 

  103. J. Van de Vondel, C.C. de Souza Silva, B.Y. Zhu, M. Morelle, V.V. Moshchalkov, Phys. Rev. Lett. 94 (2005)

    Google Scholar 

  104. C.C. de Souza Silva, J. Van de Vondel, M. Morelle, V.V. Moshchalkov, Nature, 400, 651 (2006)

    Article  Google Scholar 

  105. S. Ooi, T. Mochikua, K. Hirataa, Physica C 468 (2008)

    Google Scholar 

  106. J.E. Villegas, S. Savelev, F. Nori, E.M. Gonzalez, J.V. Anguita, R. Garcia, J.L. Vicent, Science, 302, 1188 (2003)

    Article  ADS  Google Scholar 

  107. D.E. Shalóm, H. Pastoriza, Phys. Rev. Lett. 94, 177001 (2005)

    Article  ADS  Google Scholar 

  108. Y. Togawa, K. Harada, T. Akashi, H. Kasai, T. Matsuda, F. Nori, A. Maeda, A. Tonomura, Phys. Rev. Lett. 95, 087002 (2005)

    Article  ADS  Google Scholar 

  109. K. Yu, T.W. Heitmann, C. Song, M.P. DeFeo, B.L.T. Plourde, M.B.S. Hesselberth, P.H. Kes, Phys. Rev. B 76, 220507(R) (2007)

    Google Scholar 

  110. W.K. Kwok, R.J. Olsson, G. Karapetrov, U. Welp, V. Vlasko-Vlasov, K. Kadowaki, G.W. Crabtree, Physica C 382, 137 (2002)

    Article  ADS  Google Scholar 

  111. W. Gillijns, A.V. Silhanek, V.V. Moshchalkov, C.J. Olson Reichhardt, C. Reichhardt, Phys. Rev. Lett. 99, 247002 (2007)

    Article  ADS  Google Scholar 

  112. R. Bartussek, P. Hänggi, J.G. Kissner, Europhys. Lett. 28, 459 (1994)

    Article  ADS  Google Scholar 

  113. C.C. de Souza Silva, J. Van de Vondel, B.Y. Zhu, M. Morelle, V.V. Moshchalkov, Phys. Rev. B 73, 014507 (2006)

    Article  ADS  Google Scholar 

  114. Q. Lu, C.J. Olson Reichhardt, C. Reichhardt, Phys. Rev. B 75, 054502 (2007)

    Article  ADS  Google Scholar 

  115. S.V. Dubonos, V.I. Kuznetsov, I.N. Zhilyaev, A.V. Nikulov, A.A. Firsov, JETP Lett. 77, 371 (2003)

    Article  ADS  Google Scholar 

  116. M. Morelle, N. Schildermans, V.V. Moshchalkov, Appl. Phys. Lett. 89, 1121512 (2006)

    Article  Google Scholar 

  117. N. Schildermans, A.B. Kolton, R. Salenbien, V.I. Marconi, A.V. Silhanek, V.V. Moshchalkov, Phys. Rev. B 76, 224501 (2007)

    Article  ADS  Google Scholar 

  118. W.A. Little, R.D. Parks, Phys. Rev. Lett. 9, 9 (1964)

    Article  ADS  Google Scholar 

  119. L.F. Chibotaru, A. Ceulemans, V. Bruyndoncx, V.V. Moshchalkov, Phys. Rev. Lett. 86, 1323 (2001)

    Article  ADS  Google Scholar 

  120. J. Van de Vondel, C.C. de Souza Silva, V.V. Moshchalkov, Euro. Phys. Lett. 80, 17006 (2007)

    Article  ADS  Google Scholar 

  121. G. Carneiro, Phys. Rev. B 72, 144514 (2005)

    Article  ADS  Google Scholar 

  122. C.C. de Souza Silva, A.V. Silhanek, J. Van de Vondel, W. Gillijns, V. Metlushko, B. Ilic, V.V. Moshchalkov, Phys. Rev. Lett. 98, 117005 (2007)

    Article  ADS  Google Scholar 

  123. A.V. Silhanek, N. Verellen, V. Metlushko, W. Gillijns, F. Gozzini, B. Ilic V.V. Moshchalkov, Physica C 468, 563 (2008)

    Google Scholar 

  124. S. Savel’ev, F. Marchesoni, F. Nori, Phys. Rev. Lett. 91, 010601 (2003)

    Article  ADS  Google Scholar 

  125. D. Cole, S. Bending, S. Savel’ev, A. Grigorenko, T. Tamegai, F. Nori, Nat. Mater. 5, 305 (2006)

    Article  ADS  Google Scholar 

  126. S. Savel’ev, F. Nori, Nat. Mater. 1, 179 (2002)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Alejandro V. Silhanek .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Silhanek, A.V., Van de Vondel, J., Moshchalkov, V.V. (2010). Guided Vortex Motion and Vortex Ratchets in Nanostructured Superconductors. In: Moshchalkov, V., Woerdenweber, R., Lang, W. (eds) Nanoscience and Engineering in Superconductivity. NanoScience and Technology. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15137-8_1

Download citation

Publish with us

Policies and ethics