Meissner effect in a system of coupled one-dimensional superconducting wires: Monte Carlo simulations

Abstract

Motivated by the observation of superconducting behavior in $4\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}$ carbon nanotube-zeolite composites, we use Monte Carlo simulations to evaluate the Meissner effect in a system of coupled one-dimensional superconducting wires. We model the system by using an anisotropic Ginzburg-Landau free energy functional, with distinct transverse and longitudinal coupling constants. By varying the degree of anisotropy, we obtain behaviors ranging from independent wires with suppressed superconducting transition, to an isotropic superconducting system. We numerically evaluate the Meissner effect for finite-sized superconducting domains. Comparison with the experimental data for carbon nanotube-zeolite composite shows the size of the phase-coherent, superconducting domains to be small, i.e., on the order of one or a few transverse coherence lengths. We provide a consistent estimate of the material parameters for the nanotube-zeolite composite, ranging from the penetration length of transverse magnetic field to the longitudinal and transverse coherence lengths.