Practical Guide to Quantum Phase Transitions in Quantum-Dot-Based Tunable Josephson Junctions

Superconducting quantum dots (SQDs), as generalized and tunable Josephson junctions, have potential for versatile components in electronic circuits and detectors. A key factor holding back their application is characterization, which often requires lengthy, impractical numerical methods. The authors offer simple analytical formulas that allow fast, reliable characterization of SQDs in different regimes, plus a straightforward and general method to locate the quantum phase transition from finite-temperature experimental data. These tools will dramatically speed up the characterization of real devices, and provide a handy framework to predict and refine the properties of these devices.