Nucleation of superconductivity in mesoscopic star-shaped superconductors

Abstract.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 $\xi (T)$. 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.