Nucleation of superconductivity in mesoscopic star-shaped superconductors

We study the phase transition of a star-shaped superconductor, which covers smoothly the range from zero to two dimensions with respect to the superconducting coherence length \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\xi (T)$\end{document}. Detailed measurements and numerical calculations show that the nucleation of superconductivity in this device is very inhomogeneous: the superconducting order parameter is strongly enhanced and mostly robust in regions close to multiple boundaries. The strong inhomogeneity of the order parameter results in a rich structure of the superconducting transition as a function of temperature and magnetic field.