Power Law Blinking Quantum Dots: Stochastic and Physical Models

TL;DR

This paper investigates the nonergodic blinking behavior of quantum dots using stochastic and physical models, revealing that simple diffusion models cannot fully explain the observed power-law blinking statistics.

Contribution

It introduces a modified diffusion model to explain nonergodic blinking in quantum dots, supported by data showing near-identical on/off interval distributions with specific power-law exponents.

Findings

Nonergodic and aging behaviors are characterized in quantum dots.

On and off interval distributions follow similar power-law forms with exponent ~0.8.

Simple diffusion models with exponent 0.5 are insufficient to explain the data.

Abstract

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.