Micro-SQUID characteristics

We report on the dependence on field and temperature of the critical current of micro-SQUIDs: SQUIDs with diameters as small as 1 micron, using Dayem bridges as weak links. We model these SQUIDs by solving the Ginzburg-Landau equations with appropriate boundary conditions to obtain the supercurrent-phase relationships. These solutions show that the phase drops and depression of the order parameter produced by supercurrent flow are often distributed throughout the micro-SQUID structure, rather than being localized in the bridge area, for typical micro-SQUID geometries and coherence lengths. The resultant highly non-sinusoidal current-phase relationships $I_c(\phi)$ lead to reduced modulation depths and triangular dependences of the micro-SQUID critical currents on applied magnetic flux $I_c(\Phi)$. Our modelling agrees well with our measurements on both Al and Nb micro-SQUIDs.