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We present measurements of microwave-induced Shapiro steps in asuperconducting nanobridge weak link in the dissipative branch of a hystereticcurrent-voltage characteristic. We demonstrate that Shapiro steps can be usedto infer a reduced critical current and associated effective local temperature.Our observation of Shapiro steps in the dissipative branch hows that a finiteJosephson coupling exists in the dissipative state and thus can be used to putan upper limit on the effective temperature and on the size of the region thatcan be heated above the critical temperature. This work provides evidence thatJosephson behaviour can still exist in thermally-hysteretic weak link devicesand will allow extension of the temperature ranges that nanobridge based singleflux quantum circuits, nanoSQUIDs and Josephson voltage standards can be used.

Existence of Shapiro Steps in the Dissipative Regime in Superconducting Weak Links