Using fluorescent microthermal imaging we have investigated the origin of two-step behavior in I-V curves for a current-carrying YBa_2Cu_3O_x superconducting bridge. High resolution temperature maps reveal that as the applied current increases the first step in the voltage corresponds to local dissipation (hot spot), whereas the second step is associated with onset of global dissipation throughout the entire bridge. A quantitative explanation of the experimental results is provided by a simple model for an inhomogeneous superconductor, assuming that the hot spot nucleates at a location with slightly depressed superconducting properties.
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