Josephson coupling in the dissipative state of a thermally hysteretic μ -SQUID

Micron-sized superconducting interference devices ($\ensuremath{\mu}$-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. Compared to the nonhysteretic regime, this regime extends the voltage readout mode in a given $\ensuremath{\mu}$-SQUID to further lower temperatures. More importantly, the quantitative modeling of this regime incorporating both heating and phase dynamics paves the way for further optimization of $\ensuremath{\mu}$-SQUIDs for nanomagnetism.