Journal of Low Temperature Physics

, Volume 187, Issue 5–6, pp 668–676 | Cite as

Pseudogap Phenomena Near the BKT Transition of a Two-Dimensional Ultracold Fermi Gas in the Crossover Region

  • M. Matsumoto
  • R. Hanai
  • D. Inotani
  • Y. Ohashi


We investigate strong-coupling properties of a two-dimensional ultracold Fermi gas in the normal phase. In the three-dimensional case, it has been shown that the so-called pseudogap phenomena can be well described by a (non-self-consistent) T-matrix approximation (TMA). In the two-dimensional case, while this strong-coupling theory can explain the pseudogap phenomenon in the strong-coupling regime, it unphysically gives large pseudogap size in the crossover region, as well as in the weak-coupling regime. We show that this difficulty can be overcome when one improves TMA to include higher-order pairing fluctuations within the framework of a self-consistent T-matrix approximation (SCTMA). The essence of this improvement is also explained. Since the observation of the BKT transition has recently been reported in a two-dimensional \(^6\hbox {Li}\) Fermi gas, our results would be useful for the study of strong-coupling physics associated with this quasi-long-range order.


Ultracold Fermi gas Two-dimensional system BKT phase transition 



We thank H. Tajima, T. Yamaguchi, P. van Wyk , and D. Kagamihara for discussions. M. M. was supported by Graduate School Doctoral Student Aid Program from Keio University. R. H. was supported by a Grant-in-Aid for JSPS fellows. D. I. was supported by Grant-in-Aid for Young Scientists (B) (No. 16K17773) from JSPS in Japan. This work was supported by the KiPAS project in Keio university. Y.O was supported by Grant-in-Aid for Scientific Research from MEXT and JSPS in Japan (Nos. 15K00178, 15H00840, 16K05503).


  1. 1.
    V. Gurarie, L. Radzihovsky, Ann. Phys. 332, 2 (2007)ADSCrossRefGoogle Scholar
  2. 2.
    I. Bloch, J. Dalibard, W. Zwerger, Rev. Mod. Phys. 80, 885 (2008)ADSCrossRefGoogle Scholar
  3. 3.
    J.T. Stewart, J.P. Gaebler, D.S. Jin, Nature 454, 744 (2008)ADSCrossRefGoogle Scholar
  4. 4.
    J.P. Gaebler et al., Nat. Phys. 6, 569 (2010)CrossRefGoogle Scholar
  5. 5.
    K. Martiyanov, V. Makhalov, A. Turlapov, Phys. Rev. Lett. 105, 030404 (2010)ADSCrossRefGoogle Scholar
  6. 6.
    M. Feld et al., Nature 480, 75 (2011)ADSCrossRefGoogle Scholar
  7. 7.
    B. Fröhlich et al., Phys. Rev. Lett. 106, 105301 (2011)ADSCrossRefGoogle Scholar
  8. 8.
    A.T. Sommer et al., Phys. Rev. Lett. 108, 045302 (2012)ADSCrossRefGoogle Scholar
  9. 9.
    V. Makhalov, K. Martiyanov, A. Turlapov, Phys. Rev. Lett. 112, 045301 (2014)ADSCrossRefGoogle Scholar
  10. 10.
    M.G. Ries et al., Phys. Rev. Lett. 114, 230401 (2015)ADSCrossRefGoogle Scholar
  11. 11.
    P.A. Murthy et al., Phys. Rev. Lett. 115, 010401 (2015)ADSCrossRefGoogle Scholar
  12. 12.
    K. Fenech et al., Phys. Rev. Lett. 116, 045302 (2016)ADSCrossRefGoogle Scholar
  13. 13.
    V.L. Berezinskii, Sov. Phys. JETP 32, 493 (1971)ADSMathSciNetGoogle Scholar
  14. 14.
    J.M. Kosterlitz, D.J. Thouless, J. Phys. C 6, 1181 (1973)ADSCrossRefGoogle Scholar
  15. 15.
    S. Tsuchiya, R. Watanabe, Y. Ohashi, Phys. Rev. A 80, 033613 (2009)ADSCrossRefGoogle Scholar
  16. 16.
    Q.J. Chen, K. Levin, Phys. Rev. Lett. 102, 190402 (2009)ADSCrossRefGoogle Scholar
  17. 17.
    H. Hu, X.-J. Liu, P.D. Drummond, H. Dong, Phys. Rev. Lett. 104, 240407 (2010)ADSCrossRefGoogle Scholar
  18. 18.
    F. Marsiglio et al., Phys. Rev. B 91, 054509 (2015)ADSCrossRefGoogle Scholar
  19. 19.
    M. Matsumoto, D. Inotani, Y. Ohashi, Phys. Rev. A 93, 013619 (2016)ADSCrossRefGoogle Scholar
  20. 20.
    S.A. Morgan, M.D. Lee, K. Burnett, Phys. Rev. A 65, 022706 (2002)ADSCrossRefGoogle Scholar
  21. 21.
    R. Haussmann, Z. Phys. B: Condens. Matter 91, 291 (1993)ADSCrossRefGoogle Scholar
  22. 22.
    M. Bauer, M.M. Parish, T. Enss, Phys. Rev. Lett. 112, 135302 (2014)ADSCrossRefGoogle Scholar
  23. 23.
    B.C. Mulkerin et al., Phys. Rev. A 92, 063636 (2015)ADSCrossRefGoogle Scholar
  24. 24.
    N.D. Mermin, H. Wagner, Phys. Rev. Lett. 17, 1133 (1966)ADSCrossRefGoogle Scholar
  25. 25.
    P.C. Hohenberg, Phys. Rev. 158, 383 (1967)ADSCrossRefGoogle Scholar
  26. 26.
    D.J. Thouless, Ann. Phys. 10, 553 (1960)ADSMathSciNetCrossRefGoogle Scholar
  27. 27.
    J.R. Schrieffer, Theory of Superconductivity (Addison-Wesley, New York, 1964)MATHGoogle Scholar
  28. 28.
    K. Miyake, Prog. Theor. Phys. 69, 6 (1983)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Faculty of Science and TechnologyKeio UniversityYokohamaJapan

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