Localization behavior of Dirac particles in disordered graphene superlattices

TL;DR

This paper investigates how weak disorder affects the localization of Dirac particles in graphene superlattices, revealing angular-dependent delocalization resonances that could enable disorder-based filtering.

Contribution

It provides both analytical and numerical analysis of localization behavior in disordered graphene superlattices, highlighting angular-dependent effects and delocalization resonances.

Findings

Delocalization resonances occur for both scalar and vector potentials.

The Lyapunov exponent shows sharp angular dependence.

Numerical simulations confirm the potential for disorder-induced filtering.

Abstract

Graphene superlattices (GSLs), formed by subjecting a monolayer graphene sheet to a periodic potential, can be used to engineer band structures and, from there, charge transport properties, but these are sensitive to the presence of disorder. The localization behavior of massless 2D Dirac particles induced by weak disorder is studied for both scalar-potential and vector-potential GSLs, computationally as well as analytically by a weak-disorder expansion. In particular, it is investigated how the Lyapunov exponent (inverse localization length) depends on the incidence angle to a 1D GSL. Delocalization resonances are found for both scalar and vector GSLs. The sharp angular dependence of the Lyapunov exponent may be exploited to realize disorder-induced filtering, as verified by full 2D numerical wave packet simulations.