Quantum Diffusion and Localization in Disordered Electronic Systems

TL;DR

This paper investigates how electronic wave packets diffuse in disordered one-dimensional systems with power-law distributed impurities, revealing anomalous diffusion behaviors and effects of external electric fields.

Contribution

It introduces a model incorporating fractal impurity distributions and studies their impact on diffusion, highlighting novel anomalous behaviors in disordered quantum systems.

Findings

System-wide anomalous diffusion observed for certain power-law exponents.

External electric fields induce asymmetric diffusion effects.

Results relate to behaviors in quantum wells with photogenerated electron-hole plasmas.

Abstract

The diffusion of electronic wave packets in one-dimensional systems with on-site, binary disorder is numerically investigated within the framework of a single-band tight-binding model. Fractal properties are incorporated by assuming that the distribution of distances $\ell$ between consecutive impurities obeys a power law, $P(\ell) \sim \ell^{-\alpha}$. For suitable ranges of $\alpha$, one finds system-wide anomalous diffusion. Asymmetric diffusion effects are introduced through the application of an external electric field, leading to results similar to those observed in the case of photogenerated electron-hole plasmas in tilted InP/InGaAs/InP quantum wells.