1D to 3D Crossover Transition in a System of Weakly Coupled Superconducting Nanowires

Recent Results have shown the existence of superconductivity in quasi-one-dimensional systems, e.g., the 4{\AA} superconducting carbon nanotubes embedded in the aligned, linear pores of the aluminophosphate-five (AFI) zeolite. In order to understand theoretically the experimental observations on the thermal specific heat and the electrical resistance variation as a function of temperature, we have carried out Monte Carlo simulations on a Ginzburg-Landau (GL) model of Josephson-coupled superconducting nanowires. The results show that the competition between 1D fluctuations and the weak transverse Josephson coupling between the nanowires can give rise to a 1D-3D crossover transition at a temperature $T_{C} $ below the mean field $T_{C}^{O} $ of the wires. The electrical resistance can experience a sharp drop at $T_{C} $, at which point the nanowires become phase coherent. The simulated specific heat exhibits a rounded peak between $T_{C} $and $T_{C}^{O} $, whereas the phase correlation length within the ab plane diverges at $T_{C} $ from above, in a manner that is consistent with the occurrence of a BKT-transition in the ab plane. These Monte Carlo simulated behaviors are in excellent agreement with the experimental data.