Theoretical modelling of 2D SQUID arrays

Full text: Superconducting quantum interference devices (SQUIDs) are used extensively in magnetic sensing applications due to their robustness and sensitivity. Combining multiple SQUIDs into a grid-like structure, known as a SQUID or SQIF (superconducting quantum interference filter) array; has been shown to significantly improve the voltage-to-flux response of these devices, and theoretical models of these structures have also been developed for high temperature superconductors. Nevertheless, these models are based on the assumption that superconducting segments in the array are narrow compared to the hole sizes, hence neglecting flux focusing effects that arise in wider structures. In this work, we model Yttrium-Barium Copper Oxide (YBCO) thin-film dc SQUID arrays at T=77 Kelvin and validate our results with experimental measurements. We demonstrate that the device's voltage response to externally applied magnetic fields cannot be accurately computed using traditional lumped element circuits when wide busbars are present in the array. This is because of flux focusing, which significantly modifies the effective area and mutual inductances between neighbouring loops. However, using Müller's stream function approach of solving London's equations along with the junction equations of motion; we obtain accurate results for the voltage response which closely match experimental measurements. (author)