Abstract
The effect of spin-fluctuation scattering processes on the region of the superconducting phase in strongly correlated electrons (Hubbard fermions) is investigated by the diagram technique for Hubbard operators. Modified Gor’kov equations in the form of an infinitely large system of integral equations are derived taking into account contributions of anomalous components \( P_{0\sigma ,\bar \sigma 0} \) of strength operator \( \hat P \). It is shown that spinfluctuation scattering processes in the one-loop approximation for the t-t′-t″-J* model taking into account long-range hoppings and three-center interactions are reflected by normal (P 0σ, 0σ) and anomalous (\( P_{0\sigma ,\bar \sigma 0} \)) components of the strength operator. Three-center interactions result in different renormalizations of the kernels of the integral equations for the superconducting d phase in the expressions for the self-energy and strength operators. In this approximation for the d-type symmetry of the order parameter for the superconducting phase, the system of integral equations is reduced to a system of nonhomogeneous equations for amplitudes. The resultant dependences of critical temperature on the electron concentrations show that joint effect of long-range hoppings, three-center interactions, and spin-fluctuation processes leads to strong renormalization of the superconducting phase region.
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References
J. Hubbard, Proc. R. Soc. London, Ser. A 276, 238 (1963).
V. J. Emery, Phys. Rev. Lett. 58, 2794 (1987); C. M. Varma, S. Schmitt-Rink, and E. Abrahams, Solid State Commun. 62, 681 (1987).
Ya. B. Gaididei and V. M. Loktev, Phys. Status Solidi B 147, 307 (1988).
P. W. Anderson, Science (Washington) 235, 1196 (1987).
N. M. Plakida, V. Yu. Yushankhay, and I. V. Stasyuk, Physica C (Amsterdam) 162–164, 787 (1989).
Yu. A. Izyumov and B. M. Letfulov, J. Phys.: Condens. Matter 2, 8905 (1990).
V. Yu. Yushankhay, N. M. Plakida, and P. Kalinay, Physica C (Amsterdam) 174, 401 (1991).
M. A. Baranov and M. Yu. Kagan, Z. Phys. B: Condens. Matter 86, 237 (1992).
M. Yu. Kagan and T. M. Rice, J. Phys.: Condens. Matter 6, 3771 (1994).
Yu. A. Izyumov, M. I. Katsnel’son, and Yu. N. Skryabin, Magnetism of Itinerant Electrons (Nauka, Moscow, 1994) [in Russian].
N. M. Plakida, High-Temperature Superconductivity, (Springer, Berlin, 1995).
Yu. A. Izyumov, Usp. Fiz. Nauk 167(5), 465 (1997) [Phys.—Usp. 40 (5), 521 (1997)].
V. I. Belyavskiĭ, V. V. Kapaev, and Yu. V. Kopaev, Zh. Éksp. Teor. Fiz. 118(4), 941 (2000) [JETP 91 (4), 817 (2000)].
V. I. Belyavskii and Yu. V. Kopaev, Usp. Fiz. Nauk 176(5), 457 (2006) [Phys.—Usp. 49 (5), 441 (2006)].
M. Yu. Kagan, A. V. Klaptsov, I. V. Brodsky, R. Combescot, and X. Leyronas, Usp. Fiz. Nauk 176(10), 1105 (2006) [Phys.—Usp. 49 (10), 1079 (2006)].
R. O. Zaitsev, Zh. Éksp. Teor. Fiz. 68(1), 207 (1975) [Sov. Phys. JETP 41 (1), 100 (1975))]; Zh. Éksp. Teor. Fiz. 70 (3), 1100 (1976) [Sov. Phys. JETP 43 (3), 574 (1976)].
V. V. Val’kov and S. G. Ovchinnikov, Quasiparticles in Strongly Correlated Systems (Siberian Branch of the Russian Academy of Sciences, Novosibirsk, 2001) [in Russian].
Yu. A. Izyumov and Yu. N. Skryabin, Basis Models in the Quantum Theory of Magnetism (Ural Division of the Russian Academy of Sciences, Yekaterinburg, 2002) [in Russian].
R. O. Zaitsev, Diagrammatic Method in the Theory of Superconductivity and Ferromagnetism (URSS, Moscow, 2004) [in English].
V. G. Bar’yakhtar, V. E. Krivoruchko, and D. A. Yablonskiĭ, Green’s Functions in the Theory of Magnetism (Naukova Dumka, Kiev, 1984) [in Russian].
A. A. Abrikosov, L. P. Gor’kov, and I. E. Dzyaloshinskii, Quantum Field Theoretical Methods in Statistical Physics (Fizmatgiz, Moscow, 1962; Pergamon, Oxford, 1965).
V. V. Val’kov, T. A. Val’kova, D. M. Dzebisashvili, and S. G. Ovchinnikov, Pis’ma Zh. Éksp. Teor. Fiz. 75(8), 450 (2002) [JETP Lett. 75 (8), 378 (2002)].
B. Edegger, V. N. Muthukumar, C. Gros, and P. W. Anderson, Phys. Rev. Lett. 96, 207 002 (2006).
N. M. Plakida and V. S. Oudovenko, Phys. Rev. B: Condens. Matter 59, 11 949 (1999).
N. M. Plakida, L. Anton, S. Adam, and Gh. Adam, Zh. Éksp. Teor. Fiz. 124(2), 367 (2003) [JETP 97 (2), 331 (2003)].
R. O. Zaitsev, Pis’ma Zh. Éksp. Teor. Fiz. 79(3), 143 (2004) [JETP Lett. 79 (3), 113 (2004)].
R. O. Zaĭtsev, Zh. Éksp. Teor. Fiz. 125(4), 891 (2004) [JETP 98 (4), 780 (2004)].
Yu. A. Izyumov and B. M. Letfulov, J. Phys.: Condens. Matter 3, 5373 (1991).
P. Monthoux and D. Pines, Phys. Rev. B: Condens. Matter 47, 6069 (1993).
A. V. Chubukov, D. Pines, and J. Schmalian, arXiv:condmat/0201140.
V. V. Val’kov and D. M. Dzebisashvili, Pis’ma Zh. Éksp. Teor. Fiz. 77(7), 450 (2003) [JETP Lett. 77 (7), 381 (2003)].
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Original Russian Text © V.V. Val’kov, A.A. Golovnya, 2008, published in Zhurnal Éksperimental’noĭ i Teoreticheskoĭ Fiziki, 2008, Vol. 134, No. 6, pp. 1167–1180.
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Val’kov, V.V., Golovnya, A.A. Effect of spin fluctuations on the superconducting phase of Hubbard fermions in the t-t′-t″-J* model. J. Exp. Theor. Phys. 107, 996–1008 (2008). https://doi.org/10.1134/S1063776108120091
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DOI: https://doi.org/10.1134/S1063776108120091