Phase fluctuations in two coaxial quasi-one-dimensional superconducting cylindrical surfaces serving as a model system for superconducting nanowire bundles

The dimensional crossover from a 1D fluctuating state at high temperatures to a 3D phase coherent state in the low temperature regime in two coaxial weakly-coupled cylindrical surfaces formed by two-dimensional arrays of parallel nanowires is studied via an 8-state 3D-XY model. This system serves as a model for quasi-one-dimensional superconductors in the form of bundles of weakly-coupled superconducting nanowires. A periodic variation of the dimensional crossover temperature TDC is observed when the inner superconducting cylindrical surface is rotated in the angular plane. TDC reaches a maximum when the relative angle between the cylinders is 2.81°, which corresponds to the maximum separation of nanowires between the two cylindrical surfaces. We demonstrate that the relative strength of phase fluctuations in this system is controllable by the rotational angle between the two surfaces with a strong suppression of the fluctuation strength at 2.81°. The phase fluctuations are suppressed gradually upon cooling, before they abruptly vanish below TDC. Our model thus allows us to study how phase fluctuations can be suppressed in quasi-one-dimensional superconductors in order to achieve a global phase coherent state throughout the nanowire array with zero electric resistance.