Effects of critical fluctuations and dimensionality on the jump in specific heat at the superconducting transition temperature: Application to YBa2Cu_3 O_7 - \delta, Bi_2 Sr_2CaCu_2 O_8+\delta and KOs_2 O_6 compounds

TL;DR

This paper investigates how critical fluctuations and system dimensionality influence the specific heat jump at the superconducting transition in various compounds, using a renormalized Ginzburg-Landau approach to explain experimental observations.

Contribution

It introduces a self-consistent correction method within the Ginzburg-Landau framework to accurately describe fluctuation effects across different dimensions and materials.

Findings

Fluctuation effects vary with system dimensionality and microscopic parameters.

The renormalized GL model explains specific heat anomalies in high-Tc cuprates.

Corrections to critical behavior improve understanding of experimental data.

Abstract

We report on a study of the superconducting order parameter thermodynamic fluctuations in $\mathrm{YBa}_2\mathrm{Cu}_3\mathrm{O}_{7 - \delta}$, $\mathrm{Bi}_{2}\mathrm{Sr}_{2}\mathrm{CaCu}_{2}\mathrm{O}_{8+ \delta}$ and $\mathrm{KOs}_2\mathrm{O}_6$ compounds. A non-perturbative 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 (SCA) improvement on the GL theory, a technique for obtaining corrections to the asymptotic critical behavior in terms of non universal 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 cuprate superconductors and the $\beta$-pyrochlore oxides. It is clearly shown that the enhancement, suppression or rounding of the specific heat jump of high-$T_c$ cuprate superconductors at the transition are indicative of the order parameter thermodynamic fluctuations according to the dimension and the nature of interactions.