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the Auger process must have a lifetime longer than the radiative recombination time. On the other hand, the absence of Auger-like transient at low intensities shows that the extra charge cannot be present during the entire ‘off’ period. This implies that either the electron or the hole are confined to a trap state with a lifetime longer than (but of the order of) the radiative recombination time, yet orders of magnitude shorter than the duration of the ‘off’ state. Since no changes are observed in decay dynamics at excitation rates below 0 . 1, we can estimate the nonradiative recombination time of the trapped charge in the ‘off’ state as ≈ 10 τ$_{rad}$ ( ≈ 200 ns for our QDs). The above description assumes that some stochastic process randomly switches the dot between the ‘on’ state and a range of ‘off’ states. The physics of this process is responsible for the observed power law distribution of the ‘on’ and ‘off’ times. 

The proposed scheme of QDs charge kinetics is illustrated in Fig. 4. In the ‘on’ state the dynamics is conventional (see Fig. 4 a); at low intensities the transient dynamics shows the decay rate of the single exciton k$_{r}$ , while at higher intensities the Auger recombination with the decay rate k$_{Aug}$ takes over. The above random process ‘turns off’ the QD fluorescence by opening a transition channel into a trap state either for electrons or for holes. Thus, rapid trapping at a rate k$_{tr}$ , corresponding to hundreds of picoseconds, inhibits QD luminescence. 

