Abstract
We have studied disordering effects on the coefficients of Ginzburg–Landau expansion in powers of superconducting order parameter in the attractive Anderson–Hubbard model within the generalized DMFT+Σ approximation. We consider the wide region of attractive potentials U from the weak coupling region, where superconductivity is described by BCS model, to the strong coupling region, where the superconducting transition is related with Bose–Einstein condensation (ВЕС) of compact Cooper pairs formed at temperatures essentially larger than the temperature of superconducting transition, and a wide range of disorder—from weak to strong, where the system is in the vicinity of Anderson transition. In the case of semielliptic bare density of states, disorder’s influence upon the coefficients A and В of the square and the fourth power of the order parameter is universal for any value of electron correlation and is related only to the general disorder widening of the bare band (generalized Anderson theorem). Such universality is absent for the gradient term expansion coefficient C. In the usual theory of “dirty” superconductors, the С coefficient drops with the growth of disorder. In the limit of strong disorder in BCS limit, the coefficient С is very sensitive to the effects of Anderson localization, which lead to its further drop with disorder growth up to the region of the Anderson insulator. In the region of BCS–ВЕС crossover and in ВЕС limit, the coefficient С and all related physical properties are weakly dependent on disorder. In particular, this leads to relatively weak disorder dependence of both penetration depth and coherence lengths, as well as of related slope of the upper critical magnetic field at superconducting transition, in the region of very strong coupling.
Similar content being viewed by others
References
A. A. Abrikosov and L. P. Gor’kov, Sov. Phys. JETP 9, 220 (1959).
A. A. Abrikosov and L. P. Gor’kov, Sov. Phys. JETP 9, 1090 (1959).
L. P. Gor’kov, Sov. Phys. JETP 36, 1364 (1959).
A. A. Abrikosov and L. P. Gor’kov, Sov. Phys. JETP 12, 1243 (1961).
P. W. Anderson, J. Phys. Chem. Solids 11, 26 (1959).
P. G. de Gennes, Superconductivity of Metals and Alloys (W. A. Benjamin, New York, 1966).
L. N. Bulaevskii and M. V. Sadovskii, JETP Lett. 39, 640 (1984).
L. N. Bulaevskii and M. V. Sadovskii, J. Low. Temp. Phys. 59, 89 (1985).
M. V. Sadovskii, Phys. Rep. 282, 226 (1997); arXiv:cond-mat/9308018
M. V. Sadovskii, Superconductivity and Localization (World Scientific, Singapore, 2000).
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. 1297, 339 (2010); arXiv: 1004.5069.
N. A. Kuleeva, E. Z. Kuchinskii, and M. V. Sadovskii, J. Exp. Theor. Phys. 119, 264 (2014); arXiv: 1401.2295.
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. Prushke, and V. I. Anisimov, Phys. Rev. B 72, 155105 (2005); arXiv: cond-mat/0508585.
E. Z. Kuchinskii, I. A. Nekrasov, and M. V. Sadovskii, Low Temp. Phys. 32, 398 (2006); arXiv: cond-mat/0510376.
E. Z. Kuchinskii, I. A. Nekrasov, and M. V. Sadovskii, Phys. Usp. 53, 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 and M. V. Sadovskii, J. Exp. Theor. Phys. 122, 509 (2016); arXiv:1507.07654.
E. Z. Kuchinskii, I. A. Nekrasov, and M. V. Sadovskii, Phys. Rev. B 75, 115102 (2007); arXiv:cond-mat/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.
E. Z. Kuchinskii, N. A. Kuleeva, and M. V. Sadovskii, J. Exp. Theor. Phys. 122, 375 (2016); arXiv:1507.07649.
E. Z. Kuchinskii, N. A. Kuleeva, and M. V. Sadovskii, J. Low Temp. Phys. 43, 17 (2017); arXiv: 1606.05125.
L. P. Gor’kov and I. E. Dzyaloshinskii, Quantum Field Theoretical Methods in Statistical Physics (Pergamon Press, Oxford, 1965).
M. V. Sadovskii, Diagrammatics (World Scientific, Singapore, 2006).
R. Bulla, T. A. Costi, and T. Pruschke, Rev. Mod. Phys. 60, 395 (2008)
D. Vollhardt and P. Wölfle, Phys. Rev. B 22, 4666 (1980); Phys. Rev. Lett. 48, 699 (1982).
P. Wölfle and D. Vollhardt, in Anderson Localization, Ed. by Y. Nagaoka and H. Fukuyama, Springer Ser. Solid State Sci. 39, 26 (1982).
A. V. Myasnikov and M. V. Sadovskii, Sov. Phys. Solid State 24, 2033 (1982)
E. A. Kotov and M. V. Sadovskii, Zs. Phys. B 51, 17 (1983).
M. V. Sadovskii, in Soviet Scientific Reviews–Physics Reviews, Ed. I. M. Khalatnikov (Harwood Academic, New York, 1986), vol. 7, p. 1.
D. Vollhardt and P. Wölfle, in Electronic Phase Transitions, Ed. by W. Hanke and Yu. V. Kopaev (North–Holland, Amsterdam, 1992), vol. 32, p. 1.
L. N. Bulaevskii and M. V. Sadovskii, JETP Lett. 43, 99 (1986).
L. N. Bulaevskii, S. V. Panyukov, and M. V. Sadovskii, Sov. Phys. JETP 65, 380 (1987).
Author information
Authors and Affiliations
Corresponding author
Additional information
Published in Russian in Zhurnal Eksperimental’noi i Teoreticheskoi Fiziki, 2017, Vol. 152, No. 1, pp. 133–146.
Rights and permissions
About this article
Cite this article
Kuchinskii, E.Z., Kuleeva, N.A. & Sadovskii, M.V. Ginzburg–Landau expansion in strongly disordered attractive Anderson–Hubbard model. J. Exp. Theor. Phys. 125, 111–122 (2017). https://doi.org/10.1134/S1063776117060139
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1063776117060139