A thermal model with AC Josephson effect for a shunted superconducting weak-link

Superconducting weak-link (WL), behaving like a Josephson junction (JJ), is fundamental to many superconducting devices such as nanoSQUIDs, single-photon detectors, and bolometers. The interplay between unique nonlinear dynamics inevitable Joule heating in JJ leads new characteristics. Here, we report time-dependent model incorporating thermal effect the AC regime for WL shunted by resistor together with an inductor investigate well resulting current-voltage We find that dynamic where phase temperature oscillate simply widens due pure resistive shunt. However, significant inductive time-scale shunt loop, competing time-scale, introduces high-frequency relaxation oscillations regime. Based on numerical analysis, present state diagrams different parameter regimes. Our guide better controlling parameters experiments of WL-based devices.