Abstract
The post Gaussian effective potential in D=3 and D=2+2ε are evaluated for the Ginzburg—Landau theory of superconductivity. It is shown that, the next order correction to the Gaussian approximation of the Ginzburg—Landau parameter κ is significant.This strongly indicates that strong correlations play dominant role in high T c superconductivity. In D=2+2ε fractal dimensions Ginzburg Landau parameter turned out to be sensitive to ε and the contribution of the post Gaussian term is larger than that for D = 3. Adjusting ε to the recent experimental data on κ(T) for high — T c cuprate superconductor Tl 2 Ca 2 Ba 2 Cu 3 O 10(Tℓ − 2223), we find that ε=0.21 is the best choice for this material. These results clearly show that, in order to understand high — T c superconductivity, it is necessary to include the fluctuation contribution as well as the contribution from the dimensionality of the sample. The method gives a theoretical tool to estimate the effective dimensionality of the samples.
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Rakhimov, A., Yee, J.H., Kim, C.K. (2006). Ginzburg Landau theory of superconductivity: Beyond the post Gaussian approximation. In: Khanna, F., Matrasulov, D. (eds) Non-Linear Dynamics and Fundamental Interactions. NATO Science Series II: Mathematics, Physics and Chemistry, vol 213. Springer, Dordrecht. https://doi.org/10.1007/1-4020-3949-2_24
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DOI: https://doi.org/10.1007/1-4020-3949-2_24
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