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Ginzburg Landau theory of superconductivity at fractal dimensions

Chul Koo Kim·A. Rakhimov·Jae Hyung Yee
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Abstract

The post Gaussian effective potential in $D=2+2\veps$ dimensions is evaluated for the Ginzburg-Landau theory of superconductivity. Two and three loop integrals for the post Gaussian correction terms in $D=2+2\veps$ dimensions are calculated and $\veps$-expansion for these integrals are constructed. In $D=2+2\veps$ fractal dimensions Ginzburg Landau parameter turned out to be sensitive to $\veps$ and the contribution of the post Gaussian term is larger than that for D=3. Adjusting $\veps$ to the recent experimental data on $κ(T)$ for high -$T_c$ cuprate superconductor $Tl_2Ca_2Ba_2Cu_3O_{10} (T\cl-2223)$, we found that $\veps=0.21$ is the best choice for this material. The result clearly shows 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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Chul Koo Kim, A. Rakhimov, Jae Hyung Yee. 2004-08-28. Ginzburg Landau theory of superconductivity at fractal dimensions. https://doi.org/10.1103/physrevb.71.024518

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