A Model for dx2−y2 Superconductivity in the Strongly Correlated Fermionic System
DOI:
https://doi.org/10.15407/ujpe59.05.0487Keywords:
superconductivity, strongly correlated fermionic system, t − J model, mean-field approximationAbstract
Based on the known phenomenology of high-Tc cuprates and the available numerical calculations of the t − J model, a two-dimensional effective fermionic model with the nearest neighbor attraction is proposed. Numerical calculations suggest that the model has the dx2−y2 superconductivity (SC) in the ground state at a low fermionic density. We argue that this model captures the important physics of the dx2−y2 superconducting correlations found earlier in the t − J model by the exact diagonalization approach. Within a self-consistent RPA diagrammatic study, the density and the coupling strength dependence of the critical temperature is calculated. We also investigate the influence of the impurities on our results and show that the suppression of the superconductivity is insignificant, when the retardation effects are accounted for as opposed to the Hartree–Fock approximation.
References
A.J. Leggett, in Modern Trends in the Theory of Condensed Matter, edited by A. Pekalski and R. Przystawa, (Springer, Berlin, 1980).
R.T. Scalettar et al., Phys. Rev. Lett. 62, 1407 (1989);
https://doi.org/10.1103/PhysRevLett.62.1407
A. Moreo and D. Scalapino, Phys. Rev. Lett. 66, 946 1991); M. Randeria, N. Trivedi, A. Moreo, and R.T. Scalettar, Phys. Rev. Lett. 69, 2001 (1992).
D.J. Scalapino, Phys. Rep. 250, 331 (1995).
https://doi.org/10.1016/0370-1573(94)00086-I
N.M. Plakida, High-Temperature Superconductivity: Experiment and Theory (Springer, Berlin, 1995).
https://doi.org/10.1007/978-3-642-78406-4
C.A.R. S’a de Melo, M. Randeria, and J.R. Engelbrecht, Phys. Rev. Lett. 71, 3202 (1993).
W. Li et al., arXiv:1203.2581 (2012); A. Kordyuk, Visnyk NAN Ukrainy, No. 9, 46 (2012).
A. Kordyuk, Visnyk NAN Ukrainy, No. 9, 46 (2012).
R. Micnas et al., Rev. Mod. Phys. 62, 113 (1990);
https://doi.org/10.1103/RevModPhys.62.113
E. Dagotto et al., Phys. Rev. B 49, 3548 (1994).
https://doi.org/10.1103/PhysRevB.49.3548
S. Haas et al., Phys. Rev. B 51, 5989 (1995).
https://doi.org/10.1103/PhysRevB.51.5989
A. Sboychakov et al., Phys. Rev. B 77, 224504 (2008).
https://doi.org/10.1103/PhysRevB.77.224504
E. Dagotto, Rev. Mod. Phys. 66, 763 (1994).
https://doi.org/10.1103/RevModPhys.66.763
R. Gonczarek, M. Krzyzosiak, and A. Gonczarek, Eur. Phys. J. B 61, 299 (2008).
https://doi.org/10.1140/epjb/e2008-00072-6
E.A. Pashitskii and V.I. Pentegov, Low Temp. Phys. 34, 113, (2008).
https://doi.org/10.1063/1.2834256
M.M. Korshunov et al., JETP 99, 559 (2004).
https://doi.org/10.1134/1.1809685
Strong numerical indications of -wave SC have been found before in the related models, in particular, in the − model (see, e.g., E. Dagotto and J. Riera, Phys. Rev. Lett. 70, 682 (1993);
Y. Ohta et al., Phys. Rev. Lett. 73, 324 (1994);
https://doi.org/10.1103/PhysRevLett.73.324
A. Nazarenko et al., Phys. Rev. B 54, R768 (1996)).
https://doi.org/10.1103/PhysRevB.54.R768
E. Dagotto, A. Nazarenko, and A. Moreo, Phys. Rev. Lett. 74, 728 (1994).
https://doi.org/10.1103/PhysRevLett.73.728
E. Dagotto, A. Nazarenko, and M. Boninsegni, Phys. Rev. Lett. 73, 310 (1995);
https://doi.org/10.1103/PhysRevLett.74.310
A. Nazarenko and E. Dagotto, Phys. Rev. B 54, 13158 (1996).
https://doi.org/10.1103/PhysRevB.54.13158
C. D¨urr et al., Phys. Rev. B 63, 014505 (2001).
https://doi.org/10.1103/PhysRevB.63.014505
D. Duffy et al., Phys. Rev. B 56, 5597 (1997).
https://doi.org/10.1103/PhysRevB.56.5597
P. Monthoux and D. Pines, Phys. Rev. Lett 69, 961 (1992).
https://doi.org/10.1103/PhysRevLett.69.961
D.Z. Liu, K. Levin, and J. Maly, Phys. Rev. B 51, 8680 (1995).
https://doi.org/10.1103/PhysRevB.51.8680
S. Ovchinnikov et al., Phys. Sol. State 53, 242 (2011).
https://doi.org/10.1134/S1063783411020235
P. Monthoux and D. Scalapino, Phys. Rev. Lett. 72, 1874 (1994).
https://doi.org/10.1103/PhysRevLett.72.1874
Our numerical calculations reveal that keeping only the one-loop diagram in the effective potential produces a spurious -wave condensate.
Yu.G. Pogorelov, M.C. Santos, V.M. Loktev, Low Temp. Phys., 37, 633 (2011);
https://doi.org/10.1063/1.3651472
Yu.G. Pogorelov, V.M. Loktev, Phys. Rev. B 69, 214508 (2004).
https://doi.org/10.1103/PhysRevB.69.214508
A.A. Abrikosov, L.P. Gorkov, and I.E. Dzyaloshinsky, Methods of Quantum Field Theory in Statistical Physics (Dover, New York, 1975).
For a uniform system, the tadpole diagram including the fermionic Green's function.
Downloads
Published
How to Cite
Issue
Section
License
Copyright Agreement
License to Publish the Paper
Kyiv, Ukraine
The corresponding author and the co-authors (hereon referred to as the Author(s)) of the paper being submitted to the Ukrainian Journal of Physics (hereon referred to as the Paper) from one side and the Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, represented by its Director (hereon referred to as the Publisher) from the other side have come to the following Agreement:
1. Subject of the Agreement.
The Author(s) grant(s) the Publisher the free non-exclusive right to use the Paper (of scientific, technical, or any other content) according to the terms and conditions defined by this Agreement.
2. The ways of using the Paper.
2.1. The Author(s) grant(s) the Publisher the right to use the Paper as follows.
2.1.1. To publish the Paper in the Ukrainian Journal of Physics (hereon referred to as the Journal) in original language and translated into English (the copy of the Paper approved by the Author(s) and the Publisher and accepted for publication is a constitutive part of this License Agreement).
2.1.2. To edit, adapt, and correct the Paper by approval of the Author(s).
2.1.3. To translate the Paper in the case when the Paper is written in a language different from that adopted in the Journal.
2.2. If the Author(s) has(ve) an intent to use the Paper in any other way, e.g., to publish the translated version of the Paper (except for the case defined by Section 2.1.3 of this Agreement), to post the full Paper or any its part on the web, to publish the Paper in any other editions, to include the Paper or any its part in other collections, anthologies, encyclopaedias, etc., the Author(s) should get a written permission from the Publisher.
3. License territory.
The Author(s) grant(s) the Publisher the right to use the Paper as regulated by sections 2.1.1–2.1.3 of this Agreement on the territory of Ukraine and to distribute the Paper as indispensable part of the Journal on the territory of Ukraine and other countries by means of subscription, sales, and free transfer to a third party.
4. Duration.
4.1. This Agreement is valid starting from the date of signature and acts for the entire period of the existence of the Journal.
5. Loyalty.
5.1. The Author(s) warrant(s) the Publisher that:
– he/she is the true author (co-author) of the Paper;
– copyright on the Paper was not transferred to any other party;
– the Paper has never been published before and will not be published in any other media before it is published by the Publisher (see also section 2.2);
– the Author(s) do(es) not violate any intellectual property right of other parties. If the Paper includes some materials of other parties, except for citations whose length is regulated by the scientific, informational, or critical character of the Paper, the use of such materials is in compliance with the regulations of the international law and the law of Ukraine.
6. Requisites and signatures of the Parties.
Publisher: Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine.
Address: Ukraine, Kyiv, Metrolohichna Str. 14-b.
Author: Electronic signature on behalf and with endorsement of all co-authors.
.png){kind=small}
