Abstract
We derive a Ginzburg–Landau (GL) expansion in the disordered attractive Hubbard model within the combined Nozieres–Schmitt-Rink and DMFT+Σ approximation. Restricting ourselves to the homogeneous expansion, we analyze the disorder dependence of GL expansion coefficients for a wide range of attractive potentials U, from the weak BCS coupling region to the strong-coupling limit, where superconductivity is described by Bose–Einstein condensation (BEC) of preformed Cooper pairs. We show that for the a semielliptic “bare” density of states of the conduction band, the disorder influence on the GL coefficients A and B before quadratic and quartic terms of the order parameter, as well as on the specific heat discontinuity at the superconducting transition, is of a universal nature at any strength of the attractive interaction and is related only to the general widening of the conduction band by disorder. In general, disorder growth increases the values of the coefficients A and B, leading either to a suppression of the specific heat discontinuity (in the weak-coupling limit), or to its significant growth (in the strong-coupling region). However, this behavior actually confirms the validity of the generalized Anderson theorem, because the disorder dependence of the superconducting transition temperature T c, is also controlled only by disorder widening of the conduction band (density of states).
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
A. J. Leggett, in Modern Trends in the Theory of Condensed Matter, Ed. by A. Pekalski and J. Przystawa (Springer, Berlin, 1980).
P. Nozieres and S. Schmitt-Rink, J. Low Temp. Phys. 59, 195 (1985).
Th. Pruschke, M. Jarrell, and J. K. Freericks, Adv. Phys. 44, 187 (1995).
A. Georges, G. Kotliar, W. Krauth, and M. J. Rozenberg, Rev. Mod. Phys. 68, 13 (1996).
D. Vollhardt, in Lectures on the Physics of Strongly Correlated Systems XIV, Ed. by A. Avella and F. Mancini, AIP Conf. Proc., Vol. 1297 (Amer. Inst. Physics, Melville, New York, 2010), p. 339; arXiv: 1004.5069.
M. Keller, W. Metzner, and U. Schollwock, Phys. Rev. Lett. 86, 4612 (2001); arXiv: cond-mat/0101047.
A. Toschi, P. Barone, M. Capone, and C. Castellani, New J. Phys. 7, 7 (2005); arXiv: cond-mat/0411637v1.
J. Bauer, A. C. Hewson, and N. Dupis, Phys. Rev. B 79, 214518 (2009); arXiv: 0901.1760v2.
A. Koga and P. Werner, Phys. Rev. A 84, 023638 (2011); arXiv: 1106.4559v1.
N. A. Kuleeva, E. Z. Kuchinskii, and M. V. Sadovskii, J. Exp. Theor. Phys. 119, 264 (2014); arXiv: 1401.2295.
A. I. Posazhennikova and M. V. Sadovskii, JETP Lett. 65, 270 (1997).
F. Palestini and G. C. Strinati, arXiv: 1311.2761.
E. Z. Kuchinskii, I. A. Nekrasov, and M. V. Sadovskii, JETP Lett. 82, 198 (2005); arXiv: cond-mat/0506215.
M. V. Sadovskii, I. A. Nekrasov, E. Z. Kuchinskii, Th. Pruschke, and V. I. Anisimov, Phys. Rev. B 72, 155105 (2005); arXiv: cond-mat/0508585.
E. Z. Kuchinskii, I. A. Nekrasov, and M. V. Sadovskii, J. Low Temp. Phys. 32, 528 (2006); arXiv: condmat/0510376.
E. Z. Kuchinskii, I. A. Nekrasov, and M. V. Sadovskii, Phys. Usp. 55, 325 (2012); arXiv: 1109. 2305.
E. Z. Kuchinskii, I. A. Nekrasov, and M. V. Sadovskii, J. Exp. Theor. Phys. 106, 581 (2008); arXiv: 0706.2618.
E. Z. Kuchinskii, N. A. Kuleeva, I. A. Nekrasov, and M. V. Sadovskii, J. Exp. Theor. Phys. 110, 325 (2010); arXiv: 0908.3747.
E. Z. Kuchinskii, I. A. Nekrasov, and M. V. Sadovskii, Phys. Rev. B 75, 115102 (2007); arXiv: condmat/0609404.
E. Z. Kuchinskii, N. A. Kuleeva, and M. V. Sadovskii, JETP Lett. 100, 192 (2014); arXiv: 1406.5603.
E. Z. Kuchinskii, N. A. Kuleeva, and M. V. Sadovskii, J. Exp. Theor. Phys. 120, 1055 (2015); arXiv: 1411.1547.
R. Micnas, Acta Phys. Pol. A 100 (s), 177 (2001); arXiv: cond-mat/0211561v2.
M. Drechsler and W. Zwerger, Ann. Phys. (Leipzig) 1, 15 (1992).
S. Stintzing and W. Zwerger, Phys. Rev. B 56, 9004 (1997); arXiv: cond-mat/9703129v2.
M. V. Sadovskii, Diagrammatics (World Scientific, Singapore, 2006).
R. Bulla, T. A. Costi, and T. Pruschke, Rev. Mod. Phys. 60, 395 (2008).
M. V. Sadovskii, Superconductivity and Localization (World Scientific, Singapore, 2000).
Author information
Authors and Affiliations
Corresponding author
Additional information
The article is published in the original.
Rights and permissions
About this article
Cite this article
Kuchinskii, E.Z., Kuleeva, N.A. & Sadovskii, M.V. Attractive Hubbard model: Homogeneous Ginzburg–Landau expansion and disorder. J. Exp. Theor. Phys. 122, 375–383 (2016). https://doi.org/10.1134/S1063776116020072
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1063776116020072