Extended s-wave pairing symmetry on the triangular lattice heavy fermion system

Regular Article

Abstract

We investigate the pairing symmetry of the Kondo-Heisenberg model on triangular lattice, which is believed to capture the core competition of Kondo screening and local magnetic exchange interaction in heavy electron compounds. On the dominant background of the heavy fermion state, the introduction of the Heisenberg antiferromagnetic interaction (JH) leads to superconducting pairing instability. Depending on the strength of the interactions, it is found that the pairing symmetry favours an extended s-wave for small JH and high conduction electron density but a chiral \(d_{x^2 - y^2 } + id_{xy}\)-wave for large JH and low conduction electron density, which provides a phase diagram of pairing symmetry from the calculations of the ground-state energy. The transition between these two pairing symmetries is found to be first-order. Furthermore, we also analyze the phase diagram from the pairing strengths and find that the phase diagram obtained is qualitatively consistent with that based on the ground-state energy. In addition, we propose an effective single-band BCS Hamiltonian, which is able to describe the low-energy thermodynamic behaviors of the heavy fermion superconducting states. These results further deepen the understanding of the antiferromagnetic interaction which results in a geometric frustration for the model studied. Our work may provide a possible scenario to understand the pairing symmetry of the heavy fermion superconductivity, which is one of active issues in very recent years.

Keywords

Solid State and Materials 

References

  1. 1.
    G.R. Stewart, Rev. Mod. Phys. 73, 797 (2001)CrossRefADSGoogle Scholar
  2. 2.
    H.V. Lohneysen, A. Rosch, M. Vojta, P. Wolfle, Rev. Mod. Phys. 79, 1015 (2007)CrossRefADSGoogle Scholar
  3. 3.
    S. Doniach, Physica B+C 91, 231 (1977)CrossRefADSGoogle Scholar
  4. 4.
    C. Lacroix, M. Cyrot, Phys. Rev. B 20, 1969 (1979)CrossRefADSGoogle Scholar
  5. 5.
    L.P. Regnault, W.A.C. Erkelens, J. Rossat-Mignod, P. Lejay, J. Flouquet, Phys. Rev. B 38, 4481 (1988)CrossRefADSGoogle Scholar
  6. 6.
    C.V.J. Pierre, P. Haen, S. Pujol, Physica B 163, 463 (1990)CrossRefADSGoogle Scholar
  7. 7.
    T. Chattopadhyay, P. Burlet, J. Rossat-Mignod, H. Bartholin, C. Vettier, O. Vogt, Phys. Rev. B 49, 15096 (1994)CrossRefADSGoogle Scholar
  8. 8.
    J. Flouquet et al., Physica B 215, 77 (1995)CrossRefADSGoogle Scholar
  9. 9.
    J. Arispe, B. Coqblin, C. Lacroix, Physica B 206, 255 (1995)CrossRefADSGoogle Scholar
  10. 10.
    J. Iglesias, C. Lacroix, J. Arispe, B. Coqblin, Physica B 223, 160 (1996)CrossRefADSGoogle Scholar
  11. 11.
    C. Lacroix, J. Iglesias, J. Arispe, B. Coqblin, Physica B 230, 503 (1997)CrossRefADSGoogle Scholar
  12. 12.
    J.R. Iglesias, C. Lacroix, B. Coqblin, Phys. Rev. B 56, 11820 (1997)CrossRefADSGoogle Scholar
  13. 13.
    C. Thomas, A.S. da Rosa Simões, C. Lacroix, J.R. Iglesias, B. Coqblin, J. Magn. Magn. Mater. 372, 247 (2014)CrossRefADSGoogle Scholar
  14. 14.
    X. Montiel, S. Burdin, C. Pépin, A. Ferraz, Phys. Rev. B 90, 045125 (2014)CrossRefADSGoogle Scholar
  15. 15.
    M.Z. Asadzadeh, M. Fabrizio, F. Becca, Phys. Rev. B 90, 205113 (2014)CrossRefADSGoogle Scholar
  16. 16.
    Y. Liu, H. Li, G.-M. Zhang, L. Yu, Phys. Rev. B 86, 024526 (2012)CrossRefADSGoogle Scholar
  17. 17.
    Y. Liu, G.-M. Zhang, Y. Lu, Chin. Phys. Lett. 31, 087102 (2014)CrossRefADSGoogle Scholar
  18. 18.
    J. Otsuki, Phys. Rev. Lett. 115, 036404 (2015)CrossRefADSGoogle Scholar
  19. 19.
    P. Coleman, N. Andrei, J. Phys.: Condens. Matter 1, 4057 (1989)ADSGoogle Scholar
  20. 20.
    J.C. Xavier, Phys. Rev. B 68, 134422 (2003)CrossRefADSGoogle Scholar
  21. 21.
    P.W. Anderson, Science 235, 1196 (1987)CrossRefADSGoogle Scholar
  22. 22.
    W.E. Pickett, Rev. Mod. Phys. 61, 433 (1989)CrossRefADSGoogle Scholar
  23. 23.
    D.J.V. Harlingen, Rev. Mod. Phys. 67, 515 (1995)CrossRefADSGoogle Scholar
  24. 24.
    D.N. Basov, T. Timusk, Rev. Mod. Phys. 77, 721 (2005)CrossRefADSGoogle Scholar
  25. 25.
    P.A. Lee, N. Nagaosa, X.-G. Wen, Rev. Mod. Phys. 78, 17 (2006)CrossRefADSGoogle Scholar
  26. 26.
    M.R. Norman, Science 332, 196 (2011)CrossRefADSGoogle Scholar
  27. 27.
    J.M. Williams, A.J. Schultz, U. Geiser, K.D. Carlson, A.M. Kini, H. Hau Wang, W.-K. Kwok, M.-H. Whangbo, J.E. Schirber, Science 252, 1501 (1991)CrossRefADSGoogle Scholar
  28. 28.
    K. Takada, H. Sakurai, E. Takayama-Muromachi, F. Izumi, R.A. Dilanian, T. Sasaki, Nature 422, 53 (2003)CrossRefADSGoogle Scholar
  29. 29.
    M.L. Kiesel, C. Platt, W. Hanke, R. Thomale, Phys. Rev. Lett. 111, 097001 (2013)CrossRefADSGoogle Scholar
  30. 30.
    T. Sasaki, N. Yoneyama, A. Matsuyama, N. Kobayashi, Phys. Rev. B 65, 060505 (2002)CrossRefADSGoogle Scholar
  31. 31.
    J.G. Rau, H.-Y. Kee, Phys. Rev. Lett. 106, 056405 (2011)CrossRefADSGoogle Scholar
  32. 32.
    K. Kanoda, Physica C 282, Part 1, 299 (1997)Google Scholar
  33. 33.
    H. Kino, H. Fukuyama, J. Phys. Soc. Jpn 65, 2158 (1996)CrossRefADSGoogle Scholar
  34. 34.
    H. Kino, H. Kontani, J. Phys. Soc. Jpn 67, 3691 (1998)CrossRefADSGoogle Scholar
  35. 35.
    Y. Shimizu, K. Miyagawa, K. Kanoda, M. Maesato, G. Saito, Phys. Rev. Lett. 91, 107001 (2003)CrossRefADSGoogle Scholar
  36. 36.
    T. Itou, A. Oyamada, S. Maegawa, M. Tamura, R. Kato, J. Phys.: Condens. Matter 19, 145247 (2007)ADSGoogle Scholar
  37. 37.
    L.F. Tocchio, A. Parola, C. Gros, F. Becca, Phys. Rev. B 80, 064419 (2009)CrossRefADSGoogle Scholar
  38. 38.
    Minoru Yamashita, Norihito Nakata, Yoshinori Senshu, Masaki Nagata, Hiroshi M. Yamamoto, Reizo Kato, Takasada Shibauchi, Yuji Matsuda, Science 328, 1246 (2010)CrossRefADSGoogle Scholar
  39. 39.
    L. Balents, Nature 464, 199 (2010)CrossRefADSGoogle Scholar
  40. 40.
    M.L. Kiesel, C. Platt, W. Hanke, D.A. Abanin, R. Thomale, Phys. Rev. B 86, 020507 (2012)CrossRefADSGoogle Scholar
  41. 41.
    R. Nandkishore, L. Levitov, A. Chubukov, Nat. Phys. 8, 158 (2012)CrossRefGoogle Scholar
  42. 42.
    S. Kittaka, Y. Aoki, Y. Shimura, T. Sakakibara, S. Seiro, C. Geibel, F. Steglich, H. Ikeda, K. Machida, Phys. Rev. Lett. 112, 067002 (2014)CrossRefADSGoogle Scholar
  43. 43.
    H. Kim, M.A. Tanatar, R. Flint, C. Petrovic, R. Hu, B.D. White, I.K. Lum, M.B. Maple, R. Prozorov, Phys. Rev. Lett. 114, 027003 (2015)CrossRefADSGoogle Scholar
  44. 44.
    O. Erten, R. Flint, P. Coleman, Phys. Rev. Lett. 114, 027002 (2015)CrossRefADSGoogle Scholar
  45. 45.
    K. Masuda, D. Yamamoto, Phys. Rev. B 91, 104508 (2015)CrossRefADSGoogle Scholar
  46. 46.
    N. Read, D. Newns, J. Phys. C 16, 3273 (1983)CrossRefADSGoogle Scholar
  47. 47.
    K. Ishida, Y. Kawasaki, K. Tabuchi, K. Kashima, Y. Kitaoka, K. Asayama, C. Geibel, F. Steglich, Phys. Rev. Lett. 82, 5353 (1999)CrossRefADSGoogle Scholar
  48. 48.
    Y. Zhong, L. Zhang, H.-T. Lu, H.-G. Luo, Eur. Phys. J. B 88, 238 (2015)CrossRefGoogle Scholar
  49. 49.
    J. Hu, H. Ding, Sci. Rep. 2, 381 (2012)ADSGoogle Scholar
  50. 50.
    C. Chang-Feng, Z. Li-Yuan, J. Phys. Chem. Solids 47, 547 (1986)CrossRefADSGoogle Scholar
  51. 51.
    K. Miyake, S. Schmitt-Rink, C.M. Varma, Phys. Rev. B 34, 6554 (1986)CrossRefADSGoogle Scholar
  52. 52.
    H. Ikeda, M.-T. Suzuki, R. Arita, Phys. Rev. Lett. 114, 147003 (2015)CrossRefADSGoogle Scholar
  53. 53.
    P. Coleman, A.H. Nevidomskyy, J. Low Temp. Phys. 161, 182 (2010)CrossRefADSGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Lan Zhang
    • 1
  • Yu-Feng Wang
    • 1
  • Yin Zhong
    • 1
  • Hong-Gang Luo
    • 1
    • 2
  1. 1.Center for Interdisciplinary Studies & Key Laboratory for Magnetism and Magnetic Materials of the MoELanzhou UniversityLanzhouP.R. China
  2. 2.Beijing Computational Science Research CenterBeijingP.R. China

Personalised recommendations