Effects of critical fluctuations and dimensionality on the jump in specific heat at the superconducting transition temperature: Application to YBa_{2}Cu_{3}O_{7-δ},Bi_{2}Sr_{2}CaCu_{2}O_{8+δ}, and KOs_{2}O_{6} compounds.

We report on a study of the superconducting order parameter thermodynamic fluctuations in ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}},\phantom{\rule{0.16em}{0ex}}{\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8+\ensuremath{\delta}}$, and ${\mathrm{KOs}}_{2}{\mathrm{O}}_{6}$ 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 $\ensuremath{\beta}$-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.