Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content
Springer Nature Link
Log in

Fermi-Liquid Theory and Pomeranchuk Instabilities: Fundamentals and New Developments

  • Published:
Journal of Experimental and Theoretical Physics Aims and scope Submit manuscript

Abstract

This paper is a short review on the foundations and recent advances in the microscopic Fermi-liquid (FL) theory. We demonstrate that this theory is built on five identities, which follow from conservation of the total charge (particle number), spin, and momentum in a translationally and SU(2)-invariant FL. These identities allow one to express the effective mass and quasiparticle residue in terms of an exact vertex function and also impose constraints on the “quasiparticle” and “incoherent” (or “low-energy” and “high-energy”) contributions to the observable quantities. Such constraints forbid certain Pomeranchuk instabilities of a FL, e.g., towards phases with order parameters that coincide with charge and spin currents. We provide diagrammatic derivations of these constraints and of the general (Leggett) formula for the susceptibility in arbitrary angular momentum channel, and illustrate the general relations through simple examples treated in perturbation theory.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Notes

  1. By “lattice effects,” we mean not only anisotropy but also multiple bands, which are inherent to Dirac and Weyl materials. Our model is applicable to these materials provided that (i) they are doped and (ii) the interaction on a scale much smaller than pF, in which case inter-band coupling can be neglected.

  2. One example of such a divergence in a non-SU(2)-symmetric system is the ferromagnetic instability of a FL with Rashba spin-orbit coupling, in which case the entire spin susceptibility comes from high-energy fermions [34–36].

REFERENCES

  1. E. M. Lifshits and L. P. Pitaevski, Course of Theoretical Physics, Vol. 9: Statistical Physics, Part 2 (Nauka, Moscow, 1978; Pergamon, New York, 1980).

  2. E. M. Livshits and L. P. Pitaevskii, Course of Theoretical Physics, Vol. 10: Physical Kinetics (Nauka, Moscow, 1979; Pergamon, Oxford, 1981).

  3. V. B. Berestetskii, E. M. Lifshitz, and L. P. Pitaevskii, Course of Theoretical Physics, Vol. 4: Quantum Electrodynamics (Nauka, Moscow, 1989; Butterworth–Heinemann, 1982).

  4. L. P. Pitaevskii and S. Stringari, Bose–Einstein Condensate and Superfluidity (Oxford Univ. Press, Oxford, 2016).

    Book  MATH  Google Scholar 

  5. L. D. Landau, Sov. Phys. JETP 3, 920 (1956).

    Google Scholar 

  6. L. D. Landau, Sov. Phys. JETP 5, 101 (1957).

    Google Scholar 

  7. L. D. Landau, Sov. Phys. JETP 8, 70 (1959).

    Google Scholar 

  8. A. Abrikosov, L. Gorkov, and I. Dzyaloshinski, Methods of Quantum Field Theory in Statistical Physics, Dover Books on Physics Series (Dover, New York, 1975).

    MATH  Google Scholar 

  9. P. Nozieres and D. Pines, Theory of Quantum Liquids (Hachette, UK, 1999).

    MATH  Google Scholar 

  10. G. Baym and C. J. Pethick, Landau Fermi-Liquid Theory: Concepts and Applications (Wiley, New York, 1991).

    Book  Google Scholar 

  11. P. Anderson, Basic Notions of Condensed Matter Physics (Benjamin/Cummings, London, Amsterdam, Don Mills, Sydney, Tokyo, 1984).

    Google Scholar 

  12. R. Shankar, Rev. Mod. Phys. 66, 129 (1994).

    Article  ADS  Google Scholar 

  13. I. Pomeranchuk, Sov. Phys. JETP 8, 361 (1959).

    Google Scholar 

  14. L. P. Pitaevskii, Sov. Phys. JETP 10, 1267 (1960).

    MathSciNet  Google Scholar 

  15. G. Baym and S. A. Chin, Nucl. Phys. A 262, 527 (1976).

    Article  ADS  Google Scholar 

  16. E. Fradkin, S. A. Kivelson, M. J. Lawler, J. P. Eisenstein, and A. P. Mackenzie, Ann. Rev. Condens. Matter Phys. 1, 153 (2010).

    Article  ADS  Google Scholar 

  17. R. Fernandes and A. Chubukov, Rep. Progr. Phys. 80, 014503 (2017).

    Article  ADS  Google Scholar 

  18. A. J. Leggett, Phys. Rev. 140, A1869 (1965).

    Article  ADS  MathSciNet  Google Scholar 

  19. C. Wu and S.-C. Zhang, Phys. Rev. Lett. 93, 036403 (2004).

    Article  ADS  Google Scholar 

  20. C. Wu, K. Sun, E. Fradkin, and S.-C. Zhang, Phys. Rev. B 75, 115103 (2007).

    Article  ADS  Google Scholar 

  21. A. V. Chubukov and D. L. Maslov, Phys. Rev. Lett. 103, 216401 (2009).

    Article  ADS  Google Scholar 

  22. E. I. Kiselev, M. S. Scheurer, P. Wolfle, and J. Schmalian, Phys. Rev. B 95, 125122 (2017).

    Article  ADS  Google Scholar 

  23. Y.-M. Wu, A. Klein, and A. V. Chubukov, Phys. Rev. B 97, 165101 (2018).

    Article  ADS  Google Scholar 

  24. O. Vafek and A. Vishwanath, Ann. Rev. Condens. Matter Phys. 5, 83 (2014).

    Article  ADS  Google Scholar 

  25. A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, Rev. Mod. Phys. 81, 109 (2009).

    Article  ADS  Google Scholar 

  26. L. P. Pitaevskii, J. Low Temp. Phys. 164, 173 (2011).

    Article  ADS  Google Scholar 

  27. P. S. Kondratenko, Sov. Phys. JETP 19, 972 (1964).

    MathSciNet  Google Scholar 

  28. P. S. Kondratenko, Sov. Phys. JETP 20, 1032 (1965).

    MathSciNet  Google Scholar 

  29. I. Dzyaloshinskii and P. Kondratenko, Sov. Phys. JETP 43, 1036 (1976).

    ADS  Google Scholar 

  30. A. V. Chubukov, J. J. Betouras, and D. V. Efremov, Phys. Rev. Lett. 112, 037202 (2014).

    Article  ADS  Google Scholar 

  31. P. Woelfle, private commun.

  32. S. Engelsberg and J. R. Schrieffer, Phys. Rev. 131, 993 (1963).

    Article  ADS  Google Scholar 

  33. M. Fabrizio, Lecture Notes on Many-Body Theory (2013), published online.

  34. R. A. Żak, D. L. Maslov, and D. Loss, Phys. Rev. B 82, 115415 (2010).

    Article  ADS  Google Scholar 

  35. R. A. Żak, D. L. Maslov, and D. Loss, Phys. Rev. B 85, 115424 (2012).

    Article  ADS  Google Scholar 

  36. A. Ashrafi, E. I. Rashba, and D. L. Maslov, Phys. Rev. B 88, 075115 (2013).

    Article  ADS  Google Scholar 

  37. A. Leggett, Ann. Phys. 46, 76 (1968).

    Article  ADS  Google Scholar 

  38. G. D. Mahan, Many-Particle Physics (Plenum, New York, 1990).

    Book  Google Scholar 

  39. H. Ehrenreich, in Proceedings of the International School of Physics Enrico Fermi (1967), Vol. 34.

  40. G. Eliashberg, Sov. Phys. JETP 14, 886 (1962).

    Google Scholar 

  41. A. M. Finkel’stein, Int. J. Mod. Phys. B 24, 1855 (2010).

    Article  ADS  Google Scholar 

  42. A. V. Chubukov and P. Woelfle, Phys. Rev. B 89, 045108 (2014).

    Article  ADS  Google Scholar 

  43. V. Oganesyan, S. A. Kivelson, and E. Fradkin, Phys. Rev. B 64, 195109 (2001).

    Article  ADS  Google Scholar 

  44. V. A. Zyuzin, P. Sharma, and D. L. Maslov, unpublished.

  45. V. M. Galitskii, Sov. Phys. JETP 7, 104 (1957).

    Google Scholar 

  46. A. V. Chubukov and D. L. Maslov, Phys. Rev. B 81, 245102 (2010).

    Article  ADS  Google Scholar 

  47. A. A. Abrikosov and I. M. Khalatnikov, Sov. Phys. JETP 6, 888 (1958).

    ADS  Google Scholar 

  48. J. R. Engelbrecht, M. Randeria, and L. Zhang, Phys. Rev. B 45, 10135 (1992).

    Article  ADS  Google Scholar 

Download references

ACKNOWLEDGMENTS

We thank J. Schmalian, P. Woelfle, and Y. Wu for valuable discussions. The work was supported by NSF DMR-1523036 (A. V. C. and A. K.) and NSF DMR-1720816 (D. L. M.).

Author information

Authors and Affiliations

  1. Department of Physics, University of Minnesota, MN 55455, Minneapolis, USA

    A. V. Chubukov & A. Klein

  2. Department of Physics, University of Florida, P. O. Box 118440, FL 32611-8440, Gainesville, USA

    D. L. Maslov

Authors
  1. A. V. Chubukov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. Klein
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. D. L. Maslov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. V. Chubukov.

Additional information

Contribution for the JETP special issue in honor of L.P. Pitaevskii’s 85th birthday

The article is published in the original.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chubukov, A.V., Klein, A. & Maslov, D.L. Fermi-Liquid Theory and Pomeranchuk Instabilities: Fundamentals and New Developments. J. Exp. Theor. Phys. 127, 826–843 (2018). https://doi.org/10.1134/S1063776118110122

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1063776118110122

Search

Navigation