Modeling and Characterization of Capacitively Coupled rf SQUID metamaterials

The radio frequency Superconducting Quantum Interference Device (rf SQUID) has been established as a viable building block for microwave frequency metamaterials [1,2]. To increase the coupling between SQUIDs beyond that of the conventional side-by-side geometry, the SQUIDs are stacked in the third dimension in this work. The neighboring SQUIDs partially overlap, introducing significant capacitive coupling between SQUIDs. We develop a new model incorporating the capacitive coupling with the resistor-capacitor-shunted junction model. This model successfully reproduces the observed formation of multiple bands in microwave transmission measurements through the metamaterial. The different modes associated with the bands are also imaged using laser scanning microscopy with single SQUID resolution [3]. The capacitively coupled rf SQUID metamaterial design resembles a superconducting logic circuit where the superconducting wires are closely stacked in the third dimension. The qualitatively different behavior observed and modeled in this study provides insight into the effects of such dense wiring in the superconducting logic circuit.

[1] Phys. Rev. X, 3, 041029 (2013)

[2] Phys. Rev. X, 5, 041045 (2015)

[3] Appl. Phys. Lett. 114, 082601 (2019)