Shapiro steps as a thermal probe in superconducting nanobridges

We present measurements of microwave-induced Shapiro steps in a superconducting nanobridge weak link in the dissipative branch of a hysteretic current-voltage characteristic. Typically the hot-spot Joule heating in nanobridges is suggested to extend many micrometers beyond the nanobridge itself and into the superconducting electrodes heating the system above the critical temperature. We demonstrate that the Shapiro steps can be used to infer a reduced critical current and an associated local temperature. The observation of the Shapiro steps in the dissipative branch of the IVC show that a finite Josephson coupling exists in the dissipative state, and although the nanobridge is heated, our thermal model shows that the temperature remains always below the critical temperature. This work provides evidence that Josephson behaviour can remain in thermally-hysteretic nanobridges and allows extension of the temperature range that nanobridge devices (e.g., SFQ circuits, nanoSQUIDs) can be operated in.