Effects of critical fluctuations and dimensionality on the jump in specific heat at the superconducting transition temperature: Application to YBa2Cu3O7-δ, Bi2Sr2CaCu2O8+δ, and KOs2O6 compounds

We report on a study of the superconducting order parameter thermodynamic fluctuations in YBa2Cu3O7-delta, Bi2Sr2CaCu2O8+delta, and KOs2O6 compounds. A nonperturbative technique within the framework of the renormalized Gaussian approach is proposed. The essential features are reported (analytically and numerically) through Ginzburg-Landau (GL) model-based calculations which take into account both the dimension and the microscopic parameters of the system. By presenting a self-consistent approach improvement on the GL theory, a technique for obtaining corrections to the asymptotic critical behavior in terms of nonuniversal parameters is developed. Therefore, corrections to the specific heat and the critical transition temperature for one-, two-, and three-dimensional samples are found taking into account the fact that fluctuations occur at all length scales as the critical point of a system is approached. The GL model in the free-field approximation and the 3D-XY model are suitable for describing the weak and strong fluctuation regimes respectively. However, with a modified quadratic coefficient, the renormalized GL model is able to explain certain experimental observations including the specific heat of complicated systems, such as the cup-rate superconductors and the beta-pyrochlore oxides. It is clearly shown that the enhancement, suppression, or rounding of the specific heat jump of high-T-c cup-rate superconductors at the transition are indicative of the order parameter thermodynamic fluctuations according to the dimension and the nature of interactions.