Power Law Blinking Quantum Dots: Stochastic and Physical Models

We quantify nonergodic and aging behaviors of nanocrystals (or quantum dots) based on stochastic model. Ergodicity breaking is characterized based on time average intensity and time average correlation function, which remain random even in the limit of long measurement time. We argue that certain aspects of nonergodicity can be explained based on a modification of Onsager's diffusion model of an ion pair escaping neutralization. We explain how diffusion models generate nonergodic behavior, namely a simple mechanism is responsible for the breakdown of the standard assumption of statistical mechanics. Data analysis shows that distributions of on and off intervals in the nanocrystal blinking are almost identical, $\psi_{\pm}(\tau)\propto A_{\pm}\tau^{-(1+\alpha_{\pm})}$ with $A_{+}\approx A_{-}$ and $\alpha_{+}\approx\alpha_{-}=\alpha$ and $\alpha\approx0.8$. The latter exponent indicates that a simple diffusion model with $\alpha=0.5$ neglecting the electron-hole Coulomb interaction and/or tunneling, is not sufficient.