Generation of renormalized quadratic coefficient in Landau theory: Implications for specific-heat jump calculations in high-temperature superconductors
In this work, Landau's theory is revisited by renormalizing quadratic coefficients derived from nonlinear polynomial equations to account for system dimensionality. In this respect, the generated coefficients, which include an intrinsic energy parameter specific to each material, enable precise specific-heat calculations for a range of high-temperature superconductors near the superconducting transition. To that end, the change in the specific heat jump is explained phenomenologically, which applies to any spatial arrangement and electron interactions that influence system symmetries. Moreover, effects leading to rapid, non-monotonic variation in the specific heat jump, $Δ{C_p}/T_{c}$, across the transition are examined, with particular emphasis on changes attributed to the Sommerfeld coefficient in the normal state. The considerable reduction, disappearance, or significant enhancement of the specific heat anomaly at the superconducting transition is quantitatively explained by incorporating strong fluctuation corrections to the Landau theory for low-dimensional systems. Furthermore, the evolution of specific-heat jumps with system dimensionality is analyzed, and the results are discussed in relation to experimental observations of specific-heat jumps in yttrium- and bismuth-based superconductors, as well as in zero-dimensional superconductors.