International Journal of Theoretical and Mathematical Physics
p-ISSN: 2167-6844 e-ISSN: 2167-6852
2014; 4(3): 103-109
doi:10.5923/j.ijtmp.20140403.05
Ejiroghene G. Akpojotor
Physics Department, Delta State University, Abraka, 330106, Nigeria
Correspondence to: Ejiroghene G. Akpojotor, Physics Department, Delta State University, Abraka, 330106, Nigeria.
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Copyright © 2014 Scientific & Academic Publishing. All Rights Reserved.
The phase diagram of the superconducting cuprates is a manifestation of quantum phase transition (QPT). There is still controversy if the quantum fluctuations generating the pseudogap region is a precursor to the superconducting region or they are competing phases. By modelling the basic possible Hamiltonian for this class of materials as a nonlinear dynamic system, using doping as the tuning parameter, it is possible to obtain a visualized phase diagram which captures fairly the phase diagram of the superconducting cuprates. The numerical results depict that as we doped from slight to optimal, there are three quantum critical points (QCPs): the first at the QPT from the Mott insulator and antiferromagnetic (AFM) phase to the pseudogap at slight doping, the second at the QPT from the pseudogap to the superconducting phase at minimum doping and the third is a hidden QPT due to collapse of the pseudogap around optimal doping. Therefore, the results obtained here in the context of nonlinear dynamic visualization shed new light on the study of the phase diagram of the high T_{C} superconducting cuprates.
Keywords: Superconductivity, High T_{C} cuprates, Phase diagram, Doping, Nonlinear dynamics
Cite this paper: Ejiroghene G. Akpojotor, Nonlinear Dynamic Modelling and Visualization of the Phase Diagram of the High Temperature Superconducting Cuprates, International Journal of Theoretical and Mathematical Physics, Vol. 4 No. 3, 2014, pp. 103-109. doi: 10.5923/j.ijtmp.20140403.05.
Figure 1. (colour online): The transition phase diagram of high temperature superconducting cuprates showing the various phases at various temperatures and doping levels |
(1a) |
(1b) |
(2) |
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Figure 2. The damped sinusoidal curves of the normal state, that is, when there are no changes in the initial conditions so that F_{C}_{ }= 0 |
Figure 6. The nonsinusoidal curves of the nonsuperconducting state, that is, when there are changes in the initial conditions beyond optimum doping so that for F_{c} = 0.30 |