Experimental Fine Tuning of Frustration: Two-Dimensional Superconducting Network in a Magnetic Field

Abstract

This Letter reports measurements of the magnetic field dependence of the resistive critical temperature $T_c$ of a regular square network of superconducting aluminum. We find new effects of flux quantization corresonding to both integral (1, 2, 3,...) and fractional (¼, $\frac{1}{3}$, $\frac{2}{5}$, ½, $\frac{3}{5}$, $\frac{2}{3}$, $\frac{3}{4}$) numbers of flux quanta per unit cell of the network. The fractal fine structure of the upper critical-field line is identified as the edge of the Landau-level spectrum for a tight-binding problem on a square lattice.