Josephson Coupling in the Dissipative State of a Thermally Hysteretic μ-SQUID

Micron-sized superconducting interference devices ($\mu$-SQUIDs) based on constrictions optimized for minimizing thermal runaway are shown to exhibit voltage oscillations with applied magnetic flux despite their hysteretic behavior. We explain this remarkable feature by a significant supercurrent contribution surviving deep into the resistive state, due to efficient heat evacuation. A resistively shunted junction model, complemented by a thermal balance determining the amplitude of the critical current, describes well all experimental observations, including the flux modulation of the (dynamic) retrapping current and voltage by introducing a single dimensionless parameter. Thus hysteretic $\mu$-SQUIDs can be operated in the voltage read-out mode with a faster response. The quantitative modeling of this regime incorporating both heating and phase dynamics paves the way for further optimization of $\mu$-SQUIDs for nano-magnetism.