Superconducting-Normal Phase Boundary of a Fractal Network in a Magnetic Field

Experimental measurements of the superconducting-to-normal phase boundary for a Sierpenskigasket wire network are presented. The fractal phase-boundary curve, $T_c\mathrm{}\left(H\right)\mathrm{}$, shows four orders of dilational invariance and is in excellent quantitative agreement with theoretical predictions. The fracton dimension, $\bar{\overline{d}}$, has also been measured and is found to be 1.35 ± 0.02, consistent with the calculated value of 1.365 for the planar Sierpinski gasket.