Transport Length Scales in Disordered Graphene-based Materials: Strong Localization Regimes and Dimensionality Effects

TL;DR

This study numerically investigates quantum transport in disordered graphene and nanoribbons, revealing how localization lengths and transport regimes depend on disorder, dimensionality, and edge symmetry, confirming Anderson localization in these systems.

Contribution

It provides a comparative analysis of localization lengths and transport properties in 2D graphene and nanoribbons with short-range disorder, highlighting the impact of edge symmetry and dimensionality.

Findings

Localization lengths vary significantly with edge symmetry in nanoribbons.

Graphene exhibits much larger localization lengths than nanoribbons under similar disorder.

All systems show signs of Anderson localization at zero temperature.

Abstract

We report on a numerical study of quantum transport in disordered two dimensional graphene and graphene nanoribbons. By using the Kubo and the Landauer approaches, transport length scales in the diffusive (mean free path, charge mobilities) and localized regimes (localization lengths) are computed, assuming a short range disorder (Anderson-type). In agreement with localization scaling theory, the electronic systems are found to undergo a conventional Anderson localization in the zero temperature limit. Localization lengths in weakly disordered ribbons are found to differ by two orders of magnitude depending on their edge symmetry, but always remain several orders of magnitude smaller than those computed for 2D graphene for the same disorder strength. This pinpoints the role of transport dimensionality and edge effects.