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By using a Ginzburg-Landau functional in the Gaussian approximation, wecalculate the energy of superconducting fluctuations above the transition, atzero external magnetic field, of a system composed by a small number $N$ ofparallel two-dimensional superconducting planes, each of them Josephson coupledto its first neighbour, with special focus in the $N=2$ and $3$ cases. Thisallows us to obtain expressions for the critical contributions to variousobservables (fluctuation specific heat and magnetic susceptibility andAslamazov-Larkin paraconductivity). Our results suggest that these systems maydisplay deviations from pure 2D behaviour and interesting crossover effects,with both similitudes and differences to those known to occur ininfinite-layers superconductors. Some challenges for future related researchare also outlined.

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