Statistics of thermomagnetic breakdown in Nb superconducting films

As dissimilar as they might appear, lightning during a dielectric breakdown, failure of interconnects in integrated circuits, snow avalanches on mountain slopes, or popcorn explosion share a common physics ground corresponding to the triggering of a catastrophic event when a threshold stress is exceeded. Interestingly, even if the same experience is repeated under identical environmental conditions, the event will not happen at exactly the same threshold stress. The question as to whether the statistical distribution of this threshold stress follows a universal law for all phenomena is experimentally difficult to answer, since exceeding the threshold point brings along dramatic consequences leading to irreversible changes in the system. Remarkably, superconducting materials offer a unique opportunity to investigate the statistical distribution of similar catastrophic events consisting of non-destructive magnetic flux avalanches in the same sample and thus ruling out the spreading factors associated to unavoidable uncontrollable variations in the replicas of the system.

Using the magneto-optical imaging technique to record images of the magnetic field in a superconducting Nb sample, we cycled 2000 times the same thermomagnetic breakdown experiment under identical conditions. Based on this experience, we determined the probability density function of the threshold field of thermomagnetic breakdown and tracked its temperature dependence with unprecedented resolution. Strikingly, we identified a bimodal distribution of the threshold field, with a transition from filamentary to dendritic branching avalanches, representing a unique fingerprint associated to avalanches initiated by a thermomagnetic instability, with no counterpart in other catastrophic events such as earthquakes or granular avalanches.