Dimensional crossovers in the Gaussian critical fluctuations above $T_c$ of two-layer and three-layer superconductors

TL;DR

This paper investigates the fluctuation phenomena above the critical temperature in multi-layer superconductors using a Gaussian Ginzburg-Landau model, revealing crossover effects between two-dimensional and three-dimensional behaviors.

Contribution

It provides analytical expressions for fluctuation-induced observables in two- and three-layer superconductors, highlighting dimensional crossover effects.

Findings

Deviations from pure 2D behavior in layered systems

Crossover effects between 2D and 3D fluctuation regimes

Analytical formulas for specific heat, susceptibility, and paraconductivity

Abstract

By using a Ginzburg-Landau functional in the Gaussian approximation, we calculate the energy of superconducting fluctuations above the transition, at zero external magnetic field, of a system composed by a small number $N$ of parallel two-dimensional superconducting planes, each of them Josephson coupled to its first neighbour, with special focus in the $N=2$ and $3$ cases. This allows us to obtain expressions for the critical contributions to various observables (fluctuation specific heat and magnetic susceptibility and Aslamazov-Larkin paraconductivity). Our results suggest that these systems may display deviations from pure 2D behaviour and interesting crossover effects, with both similitudes and differences to those known to occur in infinite-layers superconductors. Some challenges for future related research are also outlined.