Self-consistent analysis of the critical temperature shift in layer superconductors

Abstract

We present a self-consistent analysis of the fluctuation-induced shift of the superconducting critical temperature in layered superconductors within the time-dependent Ginzburg–Landau Lawrence–Doniach framework. Using the self-consistent Gaussian approximation, we derive explicit analytical expressions for the shift of the superconducting critical temperature that incorporate the contributions of order parameter fluctuations. Explicit results for two-dimensional and three-dimensional superconductor are also given. We reveal a fundamental dimensional crossover: while the Ginzburg–Levanyuk number Gi, which characterizes the width of the fluctuation-dominated critical region, alone governs the suppression of the critical temperature in three-dimensional (3D) superconductors, the suppression in two-dimensional (2D) and layered superconductors depends additionally on the material’s geometry, namely the layer thickness and interplane spacing. Physically, a reduction in interplane spacing or an increasing in layer thickness suppresses superconducting fluctuations, which in turn diminishes the suppression of the transition temperature. Our theoretical results are consistent with thermodynamic analysis and formulated using experimentally measurable parameters, offering a systematic approach for analyzing fluctuation phenomena in highly anisotropic superconductors and artificially layered materials.