Skip to main content
SpringerLink
Log in
Book cover

Non-Centrosymmetric Superconductors pp 129–154Cite as

Basic Theory of Superconductivity in Metals Without Inversion Center

  • Chapter
  • First Online:

Part of the book series: Lecture Notes in Physics ((LNP,volume 847))

Abstract

This Chapter gives a brief introduction to some basic aspects metals and superconductors in crystals without inversion symmetry. In the first part we analyze some normal state properties which arise through antisymmetric spin-orbit coupling existing in non-centrosymmetric materials and show its influence on the de Haas–van Alphen effect. For the superconducting phase we introduce a multi-band formulation which naturally arises due the spin splitting of the bands by spin-orbit coupling. It will then be shown how the states can be symmetry classified and their relation to the original classification in even-parity spin-singlet and odd-parity spin-triplet pairing states. The general Ginzburg–Landau functional will be derived and applied to the nucleation of superconductivity in a magnetic field. It will be shown that magneto-electric effects can modify the standard paramagnetic limiting behavior drastically.

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

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   79.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   99.99
Price excludes VAT (USA)
  • Compact, lightweight 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

Learn about institutional subscriptions

Notes

  1. 1.

    The interband pairing leads to the interesting possibility of existence of nonuniform superconducting states even in the absence of external magnetic fields [52]. These states, however, could be realized in the noncentrosymmetric compounds with the SO band splitting smaller than the superconducting critical temperature. To the best of our knowledge, in all noncentrosymmetric compounds discovered to date the relation between the two energy scales is exactly the opposite: the SO band splitting exceeds all superconducting energy scales by order of magnitude, completely suppressing the interband pairing, both uniform and nonuniform.

References

  1. Bauer, E., Hilscher, G., Michor, H., Paul Ch., Scheidt, E.W., Gribanov, A., Seropegin Yu., Noël, H., Sigrist, M., Rogl, P.: Phys. Rev. Lett. 92, 027003 (2004)

    Article  ADS  Google Scholar 

  2. Akazawa, T., Hidaka, H., Fujiwara, T., Kobayashi, T.C., Yamamoto, E., Haga, Y., Settai, R., Onuki, Y.: J. Phys.: Condens. Matter 16, L29 (2004)

    Article  ADS  Google Scholar 

  3. Kimura, N., Ito, K., Saitoh, K., Umeda, Y., Aoki, H., Terashima, T.: Phys. Rev. Lett. 95, 247004 (2005)

    Article  ADS  Google Scholar 

  4. Sugitani, I., Okuda, Y., Shishido, H., Yamada, T., Thamizhavel, A., Yamamoto, E., Matsuda, T.D., Haga, Y., Takeuchi, T., Settai, R., Onuki, Y.: J. Phys. Soc. Jpn. 75, 043703 (2006)

    Article  ADS  Google Scholar 

  5. Amano, G., Akutagawa, S., Muranaka, T., Zenitani, Y., Akimitsu, J.: . J. Phys. Soc. Jpn. 73, 530 (2004)

    Article  Google Scholar 

  6. Togano, K., Badica, P., Nakamori, Y., Orimo, S., Takeya, H., Hirata, K.: Phys. Rev. Lett. 93, 247004 (2004)

    Article  ADS  Google Scholar 

  7. Badica, P., Kondo, T., Togano, K.: J. Phys. Soc. Jpn. 74, 1014 (2005)

    Article  ADS  Google Scholar 

  8. Schuck, G., Kazakov, S.M., Rogacki, K., Zhigadlo, N. D., Karpinski, J.: Phys. Rev. 73, 144506 (2006)

    Article  Google Scholar 

  9. Bulaevskii, L.N., Guseinov, A.A., Rusinov, A.I.: Sov. Phys. JETP 44, 1243 (1976)

    ADS  Google Scholar 

  10. Levitov, L.S., Nazarov Yu.V., Eliashberg, G.M.: JETP Letters 41, 445 (1985)

    ADS  Google Scholar 

  11. Edel’stein, V.M.: Sov. Phys. JETP 68, 1244 (1989)

    Google Scholar 

  12. Gor’kov, L.P., Rashba, E.I.: Phys. Rev. Lett. 87, 037004 (2001)

    Article  ADS  Google Scholar 

  13. Mineev, V.P.: JETP Letters 57, 680 (1993)

    ADS  Google Scholar 

  14. Mineev, V.P.: Physica B 199–200, 215 (1994)

    Article  ADS  Google Scholar 

  15. Mineev, V.P., Samokhin, K.V.: Sov. Phys. JETP 78, 401 (1994)

    ADS  Google Scholar 

  16. Edel’stein, V.M.: Phys.Rev.Lett. 75, 2004 (1995)

    Article  ADS  Google Scholar 

  17. Edel’stein, V.M.: . J. Phys. Condens. Matter 8, 339 (1996)

    Article  ADS  Google Scholar 

  18. Samokhin, K.V., Zijlstra, E.S., Bose, S.K.: Phys. Rev. B 69, 094514 (2004) See also Erratum 70, 069902(E) (2004)

    Article  ADS  Google Scholar 

  19. Sergienko, I.A., Curnoe, S.H.: Phys. Rev. B 70, 214510 (2004)

    Article  ADS  Google Scholar 

  20. Mineev, V.P.: Int. J. Mod. Phys. B 18, 2963 (2004)

    Article  ADS  MATH  Google Scholar 

  21. Yip, S.K.: Phys. Rev. B 65, 144508 (2002)

    Article  ADS  Google Scholar 

  22. Barzykin, V., Gor’kov, L.P.: Phys. Rev. Lett. 89, 227002 (2002)

    Article  ADS  Google Scholar 

  23. Dimitrova, O.V., Feigel’man, M.V.: Pis’ma v ZhETF 78, 1132 (2003)

    Google Scholar 

  24. Dimitrova, O.V., Feigel’man, M.V.: Phys. Rev. B 76, 014522 (2007)

    Article  ADS  Google Scholar 

  25. Edel’stein, V.M.: Phys. Rev. B 67, 020505 (2003)

    Article  Google Scholar 

  26. Samokhin, K.V.: Phys. Rev. B 70, 104521 (2004)

    Article  ADS  Google Scholar 

  27. Frigeri, P.A., Agterberg, D.F., Koga, A., Sigrist, M.: Phys. Rev. Lett. 92, 097001 (2004) See also Erratum 93: 099903(E) (2004)

    Article  ADS  Google Scholar 

  28. Mineev, V.P.: Phys. Rev B 71, 012509 (2005)

    Article  ADS  Google Scholar 

  29. Kaur, R.P., Agterberg, D.F., Sigrist, M.: Phys. Rev. Lett. 94, 137002 (2005)

    Article  ADS  Google Scholar 

  30. Fujimoto, S.: Phys. Rev B 72, 024515 (2005)

    Article  ADS  Google Scholar 

  31. Oka, M., Ishioka, M., Machida, K.: Phys. Rev B 73, 214509 (2006)

    Article  ADS  Google Scholar 

  32. Agterberg, D.F., Kaur, R.P.: Phys. Rev B 75, 064511 (2007)

    Article  ADS  Google Scholar 

  33. Frigeri, P.A., Agterberg, D.F., Sigrist, M.: New J. Phys. 6, 115 (2004)

    Article  ADS  Google Scholar 

  34. Samokhin, K.V.: Phys. Rev. Lett. 94, 027004 (2005)

    Article  ADS  Google Scholar 

  35. Samokhin, K.V.: Phys. Rev. B 76, 094516 (2007)

    Article  MathSciNet  ADS  Google Scholar 

  36. Fujimoto, S.: Phys. Rev. B 76, 184504 (2007)

    Article  ADS  Google Scholar 

  37. Yokoyama, T., Tanaka, Y., Inoue, J.: Phys. Rev. B 72, 220504(R) (2005)

    ADS  Google Scholar 

  38. Borkje, K., Sudbo, A.: Phys. Rev. B 74, 054506 (2006)

    Article  ADS  Google Scholar 

  39. Iniotakis, C., Hayashi, N., Sawa, Y., Yokoyama, T., May, U., Tanaka, Y., Sigrist, M.: Phys. Rev. B 76, 012501 (2007)

    Article  ADS  Google Scholar 

  40. Vorontsov, A.V., Vekhter, i., Eshrig, M.: Phys. Rev. Lett. 101, 127003 (2008)

    Article  ADS  Google Scholar 

  41. Chi-Ken Lu, Sungkip Yip: Phys. Rev. B 78, 132502 (2008)

    Google Scholar 

  42. Hayashi, N., Wakabayashi, K., Frigeri, P.A., Sigrist, M.: Phys. Rev. B 73, 024504 (2006)

    Article  ADS  Google Scholar 

  43. Chi-Ken Lu, Sungkip Yip: Phys. Rev. B 77, 054515 (2008)

    Google Scholar 

  44. Edel’stein, V.M.: Phys. Rev. B 72, 172501 (2005)

    Article  ADS  Google Scholar 

  45. Frigeri, P.A., Agterberg, D.F., Milat, I., Sigrist, M.: Eur. Phys. J. B 54, 435 (2006)

    Article  ADS  Google Scholar 

  46. Mineev, V.P., Samokhin, K.V.: Phys. Rev. B 75, 184529 (2007)

    Article  ADS  Google Scholar 

  47. Samokhin, K.V.: Phys. Rev. B 78, 224520 (2008)

    Article  ADS  Google Scholar 

  48. Samokhin, K.V.: Phys. Rev. B 78, 144511 (2008)

    Article  ADS  Google Scholar 

  49. Samokhin, K.V.: Phys. Rev. B 72, 054514 (2005)

    Article  ADS  Google Scholar 

  50. Hayashi, N., Wakabayashi, K., Frigeri, P.A., Sigrist, M.: Phys. Rev. B 73, 092508 (2006)

    Article  ADS  Google Scholar 

  51. Samokhin, K.V., Mineev, V.P.: Phys. Rev. B 77, 104520 (2008)

    Article  ADS  Google Scholar 

  52. Mineev, V.P., Samokhin, K.V.: Phys. Rev. B 78, 144503 (2008)

    Article  ADS  Google Scholar 

  53. Dresselhaus, G.: Phys. Rev. 100, 580 (1955)

    Article  ADS  MATH  Google Scholar 

  54. Roth, M.: Phys. Rev. 173, 755 (1968)

    Article  ADS  Google Scholar 

  55. Rashba, E.I.: Fiz. Tverd. Tela (Leningrad) 2, 1224 (1960)

    Google Scholar 

  56. Rashba, E.I.: Sov. Phys. Solid State 2, 1109 (1960)

    Google Scholar 

  57. Mineev, V.P., Samokhin, K.V.: Phys. Rev. B 72, 212504 (2005)

    Article  ADS  Google Scholar 

  58. Lifshitz, E.M., Pitaevskii, L.P.: Statistical Physics Part 2. Butterworth-Heinemann, Oxford (1995)

    Google Scholar 

  59. Mikitik, G.P., Sharlai Yu.V.: Phys. Rev. Lett. 82, 2147 (1999)

    Article  ADS  Google Scholar 

  60. Haldane F.D.M., Phys. Rev. Lett. 93, 206602, (2002)

    Google Scholar 

  61. Hashimoto, S., Yasuda, T., Kubo, T., Shishido, H., Ueda, T., Settai, R., Matsuda, T.D., Haga, Y., Harima, H., Onuki, Y.: J. Phys.: Condens. Matter 16, L287 (2004)

    Article  ADS  Google Scholar 

  62. Suhl, H., Matthias, B.T., Walker, L.R.: Phys. Rev. Lett. 3, 552 (1959)

    Article  ADS  MATH  Google Scholar 

  63. Mineev, V. P., Samokhin, K.V.: Introduction to Unconventional Superconductivity. Gordon and Breach, London (1999)

    Google Scholar 

  64. Sigrist, M., Ueda, K.: Rev. Mod. Phys. 63, 239 (1991)

    Article  ADS  Google Scholar 

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

    Google Scholar 

  66. Yanase, Y., Sigrist, M.: J. Phys. Soc. Jpn. 76, 124709 (2007)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Commissariat à l’Energie Atomique, INAC/SPSMS, 38054, Grenoble, France

    V. P. Mineev

  2. Theoretische Physik, ETH-Zurich, 8093, Zurich, Switzerland

    M. Sigrist

Authors
  1. V. P. Mineev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Sigrist
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. P. Mineev .

Editor information

Editors and Affiliations

  1. Institute of Solid State Physics, Vienna University of Technology, Wiedner Haupstrasse 8-10, Wien, 1040, Austria

    Ernst Bauer

  2. ETH Zürich, Wolfgang-Pauli- Str. 27, Zürich, 8093, Switzerland

    Manfred Sigrist

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Mineev, V.P., Sigrist, M. (2012). Basic Theory of Superconductivity in Metals Without Inversion Center. In: Bauer, E., Sigrist, M. (eds) Non-Centrosymmetric Superconductors. Lecture Notes in Physics, vol 847. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24624-1_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-24624-1_4

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-24623-4

  • Online ISBN: 978-3-642-24624-1

  • eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)

Publish with us

Policies and ethics

Search

Navigation