Ginzburg–Landau theory of superconductivity at fractal dimensions
Chul Koo Kim, Abdulla Rakhimov, Jae Hyung Yee
DOI 10.1103/PhysRevB.71.024518 · Physical Review B
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Abstract
The post-Gaussian effective potential in D=2+2ε dimensions is evaluated for the Ginzburg–Landau theory of superconductivity. Two- and three-loop integrals for the post-Gaussian correction terms in D=2+2ε dimensions are calculated and ε expansions for these integrals are constructed. In D=2+2ε fractal dimensions the 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 the high-Tc cuprate superconductor Tl2Ca2Ba2Cu3O10, we found that ε=0.21 is the best choice for this material. The result clearly shows that, in order to understand high-Tc 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 samples.
Source-reported materials — not catalogue approval
| Formula | Reported Tc (K) | Pressure (GPa) | Type |
|---|---|---|---|
| Tl2Ca2Ba2Cu3O10 Archive — visibility unverified Source-occurrence policy only; no material identity or catalogue acceptance is inferred from the formula. | 121.5 | Pressure not reported | unknown |
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