Nanobridge superconducting quantum interference devices: Beyond the Josephson limit

Abstract

Nanoscale superconducting quantum interference devices (nano-SQUIDS) where the weak links are made from nanobridges, i.e., nanobridge SQUIDs (NBSs), are one of the most sensitive magnetometers for nanoscale magnetometry. Because of very strong nonlinearity in the nanobridge-electrode joints, the applied magnetic flux (${\mathrm{\ensuremath{\Phi}}}_{a}$)--critical current (${I}_{c}$) characteristics of NBSs differ very significantly from conventional tunnel-junction SQUIDs, especially when the nanobridges are long and/or the screening parameter is large. However, in most of the theoretical descriptions, NBSs have been treated as the conventional tunnel-junction SQUIDs, which are based on the dc Josephson effect. Here, I present a model demonstrating that for long nanobridges and/or large screening parameters the ${I}_{c}({\mathrm{\ensuremath{\Phi}}}_{a})$ of a NBS can be explained by merely considering the fluxoid quantization in the NBS loop and the energy of the NBS; it is not necessary to take the Josephson effect into consideration. I also demonstrate that using the model, one can derive useful expressions such as the modulation depth and transfer function. I discuss the role of the kinetic inductance fraction ($\ensuremath{\kappa}$) in determining ${I}_{c}({\mathrm{\ensuremath{\Phi}}}_{a})$. I compare the predictions of the present model with the experimental data already published by several groups.