Lifetime of dissipation-less state of quantum Hall electron systems in the bistable regime

Dynamic properties of the thermal bistability associated with the current-induced breakdown of the quantum Hall effect are studied. When the current increases, the critical current of transition from the dissipation-less quantum Hall state to a dissipative breakdown state at a filling factor of ν=2 is found to fluctuate from one run of current increase to another, giving compelling evidence that the transition be stochastic. The rate of escape from the dissipation-less state to the dissipative state is derived from the histogram of critical current. The escape rate is found to significantly increase as the current (or the Hall electric field) increases, indicating that the statistical probability of the dissipative state continuously increases as the current increases above a lower critical value. A consistent picture of the breakdown is suggested, where the transition is triggered by fluctuation due to heat or noise in the bistable regime.