Effect of nonlocality and anisotropy on Gaussian fluctuations around the flux-lattice state

The theory of Gaussian fluctuations around the mean-field flux-lattice state, which was developed within (Ginzburg-Landau) GL theory on the basis of Landau-level expansion of the order parameter, is applied to deriving the elastic free energy for arbitrary field orientations in a uniaxially anisotropic superconductor. It is found that the results obtained for nonlocal elastic terms coincide with those resulting from London limits, indicating the validity of the present approach in GL theory. Furthermore we show that, by examining the Gaussian fluctuation corrections to thermodynamic quantities in strongly type-II (three-dimensional) superconductors, theories formulated in infinite-κ limits are valid in fluctuation-dominated regimes of mixed states. Recent experimental results for clean samples of high-${\mathit{T}}_{\mathit{c}}$ oxides are discussed from the viewpoint of fluctuation theory.