Nano-bridge Superconducting Quantum Interference Devices: beyond the Josephson limit

TL;DR

This paper presents a new model for nano-bridge SQUIDs that explains their behavior without relying on the Josephson effect, especially for long nano-bridges and large screening parameters, enhancing understanding of their flux response.

Contribution

The paper introduces a fluxoid quantization-based model for nano-bridge SQUIDs that surpasses the traditional Josephson effect framework, applicable to long bridges and high screening conditions.

Findings

Model explains $I_{c}(\

modulation depth and transfer function.

Role of kinetic inductance fraction ($7$) in flux modulation.

Abstract

Nano-scale superconducting quantum interference devices (nano-SQUIDS) where the weak-links are made from nano-bridges --- i.e., nano-bridge--SQUIDs (NBSs) --- are one of the most sensitive magnetometers for nano-scale magnetometry. Because of very strong non-linearity in the nano-bridge--electrode joints, the applied magnetic flux ($\Phi_{a}$) -- critical current ($I_{c}$) characteristics of NBSs differ very significantly from conventional tunnel-junction-SQUIDs, especially when nano-bridges are long and/or the screening parameter is large. However, in most of the theoretical descriptions, NBSs have been treated like conventional tunnel-junction-SQUIDs, which are based on d.c. Josephson effect. Here, I present a model demonstrating that for long nano-bridges and/or large screening parameter the $I_{c}(\Phi_{a})$ 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, we can derive useful expressions like modulation depth and transfer function. I also discuss the role of kinetic inductance fraction ($\kappa$) in determining $I_{c}(\Phi_{a})$.