Ginzburg Landau theory of superconductivity: Beyond the post Gaussian approximation

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.