Skip to main content
SpringerLink
Log in

High-T c and Low-T c Superconductivity in Electron Systems with Repulsion

  • Original Paper
  • Published:
Journal of Superconductivity and Novel Magnetism Aims and scope Submit manuscript

Abstract

We demonstrate the instability of the normal state of purely repulsive fermionic systems towards the transition to the Kohn-Luttinger superconducting state. We construct the superconducting phase diagrams of these systems in the framework of the Hubbard and Shubin-Vonsovsky models on the square and hexagonal lattices. We show that an account for the long-range Coulomb interactions, as well as the Kohn- Luttinger renormalizations, lead to an increase in the critical superconducting temperatures in various materials, such as high-temperature superconductors, idealized monolayer, and bilayer of doped graphene. Additionally, we discuss the role of the structural disorder and the nonmagnetic impurities in superconducting properties of real graphene systems.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  1. Kohn, W., Luttinger, J.M.: Phys. Rev. Lett. 15, 524 (1965)

    Article  ADS  MathSciNet  Google Scholar 

  2. Fay, D., Layzer, A.: Phys. Rev. Lett. 20, 187 (1968)

    Article  ADS  Google Scholar 

  3. Kagan, M.Yu., Chubukov, A.V.: JETP Lett. 47, 614 (1988)

    ADS  Google Scholar 

  4. Baranov, M.A., Chubukov, A.V., Kagan, M.Yu: Int. J. Mod. Phys. B 6, 2471 (1992)

    Article  ADS  Google Scholar 

  5. Kagan, M. Yu., Mitskan, V. A., Korovushkin, M. M.: Phys. Usp. 58, 733 (2015)

    Article  ADS  Google Scholar 

  6. Hubbard, J.C.: Proc. R. Soc. London A 276, 238 (1963)

    Article  ADS  Google Scholar 

  7. Baranov, M. A., Kagan, M. Yu.: Z. Phys. B: Condens. Matter. 86, 237 (1992)

    Article  ADS  Google Scholar 

  8. Hlubina, R.: Phys. Rev. B 59, 9600 (1999)

    Article  ADS  Google Scholar 

  9. Raghu, S., Berg, E., Chubukov, A.V., Kivelson, S.A.: Phys. Rev. B 85, 024516 (2012)

    Article  ADS  Google Scholar 

  10. Kagan, M. Yu., Val’kov, V. V., Mitskan, V. A., Korovushkin, M. M.: JETP Lett. 97, 226 (2013). JETP, 117, 728 (2013)

    Article  ADS  Google Scholar 

  11. Raghu, S., Kivelson, S.A., Scalapino, D.J.: Phys. Rev. B 81, 224505 (2010)

    Article  ADS  Google Scholar 

  12. Alexandrov, A.S., Kabanov, V.V.: Phys. Rev. Lett. 106, 136403 (2011)

    Article  ADS  Google Scholar 

  13. Kagan, M.Yu., Efremov, D.V., Marienko, M.S., Val’kov, V.V.: JETP Lett. 93, 720 (2011)

    Article  ADS  Google Scholar 

  14. Shubin, S., Vonsowsky, S.: Proc. Roy. Soc. A 145, 159 (1934)

    Article  ADS  Google Scholar 

  15. Nandkishore, R., Levitov, L.S., Chubukov, A.V.: Nature Phys. 8, 158 (2012)

    Article  ADS  Google Scholar 

  16. Volovik, G.E.: Exotic properties of superfluid 3He. World Scientific, Singapore (1992)

    Book  Google Scholar 

  17. Black-Schaffer, A.M., Honerkamp, C.: J. Phys.: Condens. Matter. 26, 423201 (2014)

    ADS  Google Scholar 

  18. Kagan, M.Yu., Val’kov, V.V., Mitskan, V.A., Korovushkin, M.M.: Solid State Commun. 188, 61 (2014)

    Article  ADS  Google Scholar 

  19. Nandkishore, R., Thomale, R., Chubukov, A.V.: Phys. Rev. B 89, 144501 (2014)

    Article  ADS  Google Scholar 

  20. Guinea, F., Castro Neto, A.H., Peres, N.M.R.: Phys. Rev. B 73, 245426 (2006)

    Article  ADS  Google Scholar 

  21. Kagan, M.Yu., Mitskan, V.A., Korovushkin, M.M.: Eur. Phys. J. B 88, 157 (2015)

    Article  ADS  Google Scholar 

  22. Anderson, P.W.: J. Phys. Chem. Solids 11, 26 (1959)

    Article  ADS  Google Scholar 

  23. Abrikosov, A.A., Gor’kov, L.P.: Sov. Phys. JETP 12, 337 (1961)

    Google Scholar 

  24. Abrikosov, A.A., Gor’kov, L.P., Dzyaloshinski, I.E.: Quantum Field Theory in Statistical Physics. Prentice Hall, Englewood Cliffs (1963)

    MATH  Google Scholar 

  25. Posazhennikova, A.I., Sadovskii, M.V.: JETP Lett. 63, 358 (1996)

    Article  ADS  Google Scholar 

  26. Baringhaus, J., Ruan, M., Edler, F., et al.: Nature 506, 349 (2014)

    Article  ADS  Google Scholar 

  27. Bychkov, Yu.A., Gor’kov, L.P., Dzyaloshinskii, I.E.: Sov. Phys. JETP 23, 489 (1966)

    ADS  Google Scholar 

  28. Kagan, M. Yu.: Modern trends in superconductivity and superfluidity. Lecture Notes in Physics, Vol. 874. Springer, Netherlands, Dordrecht (2013)

    Book  Google Scholar 

  29. Vafek, O., Murray, J.M., Cvetkovic V.: Phys. Rev. Lett. 112, 147002 (2014)

    Article  ADS  Google Scholar 

  30. Murray, J.M., Vafek, O.: Phys. Rev. B 89, 205119 (2014)

    Article  ADS  Google Scholar 

  31. Larkin A.I., Ovchinnikov, Yu.N.: Sov. Phys. JETP 34, 1144 (1972)

    ADS  Google Scholar 

Download references

Acknowledgements

The authors are grateful to V. V. Val’kov, I. S. Burmistrov, M. V. Feigel’man, and A. Ya. Tzalenchuk for valuable remarks. This work is supported by the Russian Foundation for Basic Research (nos. 14-02-00058 and 14-02-31237). One of the authors (M. Yu. K.) gratefully acknowledges support from the Basic Research Program of the National Research University Higher School of Economics. Another one (M. M. K.) thanks the scholarship SP-1361.2015.1 of the President of Russia and the Dynasty foundation.

Author information

Authors and Affiliations

  1. P. L. Kapitza Institute for Physical Problems, 119334, Moscow, Russia

    Maxim Yu. Kagan

  2. National Research University Higher School of Economics, 109028, Moscow, Russia

    Maxim Yu. Kagan

  3. Kirensky Institute of Physics, SB RAS, 660036, Krasnoyarsk, Russia

    Vitaly A. Mitskan & Maxim M. Korovushkin

  4. Siberian State Aerospace University, 660014, Krasnoyarsk, Russia

    Vitaly A. Mitskan

  5. Nordita, KTH Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, SE-106 91, Stockholm, Sweden

    Maxim M. Korovushkin

Authors
  1. Maxim Yu. Kagan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Vitaly A. Mitskan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Maxim M. Korovushkin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Maxim Yu. Kagan.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kagan, M.Y., Mitskan, V.A. & Korovushkin, M.M. High-T c and Low-T c Superconductivity in Electron Systems with Repulsion. J Supercond Nov Magn 29, 1043–1048 (2016). https://doi.org/10.1007/s10948-016-3384-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10948-016-3384-7

Keywords

Search

Navigation