PL EN


Preferences help
enabled [disable] Abstract
Number of results
2012 | 121 | 4 | 764-784
Article title

Theory of Unconventional Superconductivity in Strongly Correlated Systems: Real Space Pairing and Statistically Consistent Mean-Field Theory - in Perspective

Authors
Content
Title variants
Languages of publication
EN
Abstracts
EN
In this brief overview we discuss the principal features of real space pairing as expressed via corresponding low-energy (t-J or periodic Anderson-Kondo) effective Hamiltonian, as well as consider concrete properties of those unconventional superconductors. We also rise the basic question of statistical consistency within the so-called renormalized mean-field theory. In particular, we provide the phase diagrams encompassing the stable magnetic and superconducting states. We interpret real space pairing as correlated motion of fermion pair coupled by short-range exchange interaction of magnitude J comparable to the particle renormalized band energy ≈ tx, where x is the carrier number per site. We also discuss briefly the difference between the real-space and the paramagnon-mediated sources of superconductivity. The paper concentrates both on recent novel results obtained in our research group, as well as puts the theoretical concepts in a conceptual as well as historical perspective. No slave-bosons are required to formulate the present approach.
Keywords
EN
Contributors
author
  • Marian Smoluchowski Institute of Physics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland
  • Faculty of Physics and Applied Computer Science, AGH University of Science and Technology, Reymonta 19, 30-059 Kraków, Poland
References
  • 1. N.F. Mott, Metal-Insulator Transitions Taylor and Francis, London 1990, (2nd ed.); M. Imada, A. Fujimori, Y. Tokura, Rev. Mod. Phys. 70, 1039 (1998). For a brief overview of an almost localized Fermi-liquid see: J. Spałek, J. Solid State Chem. 88, 70 (1990); J. Spałek, Eur. J. Phys. 21, 511 (2000). The pioneering work concerning analysis of concrete compounds as Mott-Hubbard systems was reviewed in J.B. Goodenough, Prog. Solid State Chem. 5, 149 (1971). For the first introduction of critical points in those systems see: J. Spałek, A. Datta, J.M. Honig, Phys. Rev. Lett. 59, 728 (1987); for the analysis of experimental data for V_{2}O_{3} see: P. Limelette, A. Georges, D. Jérome, P. Wzietek, P. Metcalf, J.M. Honig, Science 302, 89 (2003)
  • 2. K.J. Kugel, D.I. Khomskii, Sov. Phys. JETP 37, 725 (1973); J. Spałek, K.A. Chao, J. Phys. C 13, 5241 (1980)
  • 3. For review see: P.W. Anderson, in: Frontiers and Borderlines in Many-Particle Physics, Eds. R.A. Broglia, J.R. Schrieffer, North-Holland, Amsterdam 1988, pp. 1-40; P.A. Lee, N. Nagaosa, X.-G. Wen, Rev. Mod. Phys. 78, 17 (2006)
  • 4. B. Keimer, N. Belk, R.J. Birgeneau, A. Cassanho, C.Y. Chen, M. Greven, M.A. Kastner, A. Aharony, Y. Endoh, R.W. Erwin, G. Shirane, Phys. Rev. B 46, 14034 (1992); M.A. Kastner, R.J. Birgeneau, G. Shirane, Y. Endoh, Rev. Mod. Phys. 70, 897 (1998)
  • 5. J. Jędrak, J. Kaczmarczyk, J. Spałek, arxiv.org/abs/1008.0021; J. Jędrak, Real-space pairig in an extended t-J model, Ph.D. Thesis Jagiellonian Univesity, Krakow 2011, see http://th-www.if.uj.edu.pl/ztms/download/phdTheses/ Jakub_Jedrak_doktorat.pdf
  • 6. For t-J model: J. Spałek, Phys. Rev. B 37, 533 (1988); for review see: J. Spałek, J.M. Honig, in: Studies of High Temperature Superconductors, Vol. 8, Ed. A. Narlikar, Nova Science Publ., New York 1991, pp. 1-67. For an account of original derivation of t-J model see: J. Spałek, Acta Phys. Pol. A 111, 409 (2007) and references therein
  • 7. J. Spałek, Phys. Rev. B 38, 208 (1988); see also: J. Spałek, P. Gopalan, J. Phys. (France) 50, 2869 (1989); O. Howczak, J. Spałek, unpublished
  • 8. For the case of Mott insulators representing the parent compounds for high-T_C cuprates, the effective Heisenberg Hamiltonan was derived and analyzed in: P.W. Anderson, Phys. Rev. 115, 1 (1959); also in: Solid State Physics, Vol. 14 , Eds. F. Seitz, D. Turnbull, Academic Press, New York 1963, pp. 99-213. For revised picture see e.g. J. Zaanen, G.A. Sawatzky, J. Solid State Chem. 88, 8 (1990)
  • 9. This representation is in the case equivalent and somewhat simpler than the original Hubbard atomic representation: J. Hubbard, Proc. Roy. Soc. London A 285, 542 (1965)
  • 10. N. Fukushima, Phys. Rev. B 78, 115105 (2008). This approach was adopted to the case of Anderson lattice case by O. Howczak, unpublished
  • 11. This existence of such Hamiltonian was postulated for the first time on phenomenolgical grounds in: J. Spałek, A. Datta, J.M. Honig, Phys. Rev. B 33, 4891 (1986); J. Spałek, A. Datta, J.M. Honig , Phys. Rev. Lett. 59, 728 (1987)
  • 12. The solution results from a discussion of the authors of [5]. Very helpful was draving the analogy with the saddle-point solution of the slave-boson approach, reviewed in: Spectroscopy of the Mott Insulators and Correlated Metals, Vol. 119, Springer-Verlag, Berlin 1995, pp. 41-65. However, in contradistinction to the slave-boson theory, the present approach doe not introduce spurious condensed-Boson (ghost) fields, which introduce artifical phase-transition lines
  • 13. J. Jędrak, J. Spałek, Phys. Rev. B 83, 104512 (2011); J. Jędrak, J. Spałek, Phys. Rev. B 81, 073108 (2010)
  • 14. J. Kaczmarczyk, J. Spałek, Phys. Rev. B 84, 125140 (2011)
  • 15. O. Howczak, Ph.D. Thesis, Jagiellonian University, Kraków, 2012 (in preparation)
  • 16. The same conerns the Bardeen-Cooper-Schieffer (BCS) theory where one takes as gap Δ_{k} ≡〈c_{k↑}^{†} c_{-k↓}^{†}〉. The spin singlet nature of the state is implicitely assumed in the choice of the BCS wave function: |Ψp〉_{BCS}=∏_{k}(u_{k}+v_{k}c_{k↑}^{†} c_{-k↓}^{†})|0〉, instead: |Ψp_{BCS} = ∏_{k}[u_{k}+ 1/2 v_{k}(c_{k↑}^{†} c_{-k↓}^{†} - c_{k↓}^{†} c_{-k↑}^{†})]|0〉 for the spin singlet state c_{k↑}^{†}c_{-k↓}^{†}=-c_{k↓}^{†}c_{-k↑}^{†}
  • 17. J. Spałek, Condens. Matter Phys. 11, 455 (2008). The notion that K_{ij}<0 was assumed and reviewed in: R. Micnas, J. Ranninger, S. Robaszkiewicz, Rev. Mod. Phys. 62, 113 (1990). However, the omission in the latter paper of the exchange term in Hamiltonian (2) or (5) separates completely the appearance of superconductivity from the existence of antiferromagnetism in the low doping regime. If the electron-phonon interaction were to play a role to produce K_{ij}<0, then the most probable scenarios that we have to have simultaneously J_{ij}>0 and ~K_{ij}<0
  • 18. J. Kaczmarczyk, in: Unconventional superconductivity in correlated fermion systems, Ph.D. Thesis Jagiellonian University, Krakow 2011, see http://th-www.if.uj.edu.pl/ztms/ download/phdTheses/Jan_Kaczmarczyk_doktorat.pdf
  • 19. O. Howczak, J. Spałek, arXiv: 1110.6336
  • 20. R. Doradziński, J. Spałek, Phys. Rev. B 56, R14239 (1997); R. Doradziński, J. Spałek, Phys. Rev. B 58, 3293 (1998)
  • 21. J. Karbowski, J. Spałek, Phys. Rev. B 49, 1454 (1994); J. Karbowski, J. Spałek, Physica B 206, 716 (1995)
  • 22. A complete approach to RMFT would require solving systematically the t-J or the Anderson-Kondo model in the full Gutzwiller wave-function scheme, not only in the Gutzwiller-ansatz approximation: J. Kaczmarczyk, (unpublished)
  • 23. D. Goc-Jagło, J. Spałek, (unpublished)
  • 24. B. Edegger, V.N. Muthukumar, C. Gros, P.W. Anderson, Phys. Rev. Lett. 96, 207002 (2006)
  • 25. M.R. Norman, H. Ding, M. Randeria, J.C. Campuzano, T. Yokoya, T. Takeuchi, T. Takahashi, T. Mochiku, K. Kadowaki, P. Guptasarma, D.G. Hinks, Nature 392, 157 (1998)
  • 26. G. Rickayzen, Theory of superconductivity, John Wiley and Sons, New York 1965, p. 178
  • 27. A. Aperis, G. Varelogiannis, P.B. Littlewood, Phys. Rev. Lett. 104, 216403 (2010)
  • 28. J. Kaczmarczyk, J. Spałek, J. Phys. Condens. Matter 22, 355702 (2010); J. Kaczmarczyk, J. Spałek, Phys. Rev. B 79, 214519 (2009)
  • 29. For a recent review see: Y. Matsuda, H. Shimahara, J. Phys. Soc. Jpn. 76, 051005 (2007)
  • 30. For recent discussion of this subject see: G. Koutroulakis, M.D. Stewart, Jr., V.F. Mitrović, M. Horvatić, C. Berthier, G. Lapertot, J. Flouquet, Phys. Rev. Lett. 104, 087001 (2010); Y. Ōnuki, J. Phys. Soc. Jpn.: News and Comments 41, 1 (2009)
  • 31. A. McCollam, S.R. Julian, P.M.C. Rourke, D. Aoki, J. Flouquet, Phys. Rev. Lett. 94, 186401 (2005); I. Sheikin, Habilitation à Diriger des Recherches, Université J. Fourier, Grenoble, 2011 (unpublished)
  • 32. J. Spałek, P. Gopalan, Phys. Rev. Lett. 64, 2823 (1990); P. Korbel, J. Spałek, W. Wójcik, M. Acquarone, Phys. Rev. B 52, R2213 (1995); for review see: J. Spałek, Physica B 378-380, 654 (2006); J. Spałek, Phys. Status Solidi B 243, 78 (2006)
  • 33. M. Maśka, M. Mierzejewski, J. Kaczmarczyk, J. Spałek, Phys. Rev. B 82, 054509 (2010)
  • 34. A. Klejnberg, J. Spałek, J. Phys. Condens. Matter 11, 6553 (1999); J. Spałek, Phys. Rev. B 63, 104513, (2001); T. Nomura, K. Yamada, J. Phys. Soc. Jpn. 71, 1993 (2002). The idea of Hund's rule induced spin triplet pairing was stimulated by the discovery of ferromagnetic superconductors UGe_{2} and URhGe. In slightly different context, these ideas can be applied to spin triplet pairing in Sr_{2}RuO_{4}, cf. e.g. K.I. Wysokiński, G. Litak, J.F. Annett, B.L. Gyorffy, Phys. Status Solidi B 236, 325 (2003)
  • 35. M. Zegrodnik, J. Spałek, in preparation
  • 36. A. Klejnberg, J. Spałek, Phys. Rev. B 61, 15542 (2000); A. Klejnberg, Ph.D. Thesis, Jagiellonian University, Krakow, 2006, see: http://th-www.if.uj.edu.pl/ztms/download/ phdTheses/Andrzej_Klejnberg_doktorat.pdf
  • 37. S. Inagaki, R. Kubo, Int. J. Magnetism 4, 139 (1973)
  • 38. P.W. Anderson, Phys. Rev. 115, 2 (1959); also in: Solid State Physics, Eds: F. Seitz, D. Turnbull, Vol. 14, Academic Press, New York 1963, p. 99
  • 39. J. Spałek, A.M. Oleś, preprint SSPJU-6/1976; J. Spałek, A.M. Oleś, Physica B 86-88, 375 (1977); K.A. Chao, J. Spałek, A.M. Oleś, J. Phys. C 10, L271 (1977)
  • 40. J. Spałek, , Habilitationshrift, Jagiellonian University, Kraków 1980, (unpublished)
  • 41. J. Spałek, Acta Phys. Pol. A 111, 409 (2007)
  • 42. A.B. Harris, R.V. Lange, Phys. Rev. 157, 295 (1967)
  • 43. J. Spałek, A.M. Oleś, K.A. Chao, Phys. Rev. B 18, 3478 (1978); J. Spałek, A.M. Oleś, K.A. Chao, Phys. Status Solidi B 87, 626 (1978)
  • 44. A. Ruckenstein, P. Hirschfeld, J. Appel, Phys. Rev. B 36, 857 (1987)
  • 45. P.W. Anderson, Science 235, 1196 (1987). For an updated interpretation see: P.W. Anderson, Science 317 1705 (2007)
  • 46. F.C. Zhang, C. Gros, T.M. Rice, H. Shiba, Supercond. Sci. Technol. 1, 36 (1988); B. Edegger, V.N. Muthukumar, C. Gros, Adv. Phys. 56, 927 (2007); W.-H. Ko, C.P. Nave, P.A. Lee, Phys. Rev. B 76, 245113 (2007)
  • 47. One may therefore regard Hamiltonian ([E9]) as a reflecting strong-correlation limit of the fermion-boson model, in which the complex Bose field is with its total number of particles not conserved. For the fermion-boson model with the total number of bosons+fermions conserved, see e.g. J. Ranninger, S. Robaszkiewicz, Physica B 135, 468 (1985); T. Domański, J. Ranninger, Phys. Rev. Lett. 91, 255301 (2003). I am grateful to T. Domański for discussion of this model
Document Type
Publication order reference
Identifiers
YADDA identifier
bwmeta1.element.bwnjournal-article-appv121n4p110kz
JavaScript is turned off in your web browser. Turn it on to take full advantage of this site, then refresh the page.