Unambiguous Simulation of Diffusive Charge Transport in Disordered Nanoribbons

TL;DR

This paper introduces a new linear scaling method to simulate large disordered 2D nanoribbons, successfully capturing the ballistic, diffusive, and localized charge transport regimes with high coherence.

Contribution

The study presents a novel linear scaling approach that enables unambiguous simulation of diffusive charge transport in large disordered nanoribbons.

Findings

Successfully observed all three transport regimes in simulations

Demonstrated the crossover from ballistic to localized transport

Provided detailed characterization of diffusive transport in disordered systems

Abstract

Charge transport in disordered two-dimensional (2D) systems showcases a myriad of unique phenomenologies that highlight different aspects of the underlying quantum dynamics. Electrons in such systems undergo a crossover from ballistic propagation to Anderson localization, contingent on the system's effective coherence length. Between the extended and localized phases lies a diffusive crossover in which the charge conductivity is properly defined. The numerical observation of this regime has remained elusive because it requires fully coherent transport to be simulated in systems whose dimensions are sufficiently large to meaningfully split the mean-free path and localization length scales. To address this challenge, we employed a novel linear scaling time-resolved approach that enabled us to derive the dc-transport characteristics and observe the three expected 2D transport regimes - ballistic, diffusive, and localized.