Edge states versus diffusion in disordered graphene flakes

TL;DR

This study investigates how edge states in disordered graphene flakes behave under short-range disorder, revealing that edge states persist at weak disorder and that increased disorder can reduce localization, contrary to typical expectations.

Contribution

It demonstrates the survival of edge states at the Dirac point under weak disorder and uncovers an unusual decrease in localization with increasing disorder in graphene flakes with zig-zag edges.

Findings

Edge states persist at weak disorder in zig-zag graphene flakes.

Wavefunctions become less localized as disorder increases.

Armchair edges do not exhibit the abnormal behavior.

Abstract

We study the localization properties of the wavefunctions in graphene flakes with short range disorder, via the numerical calculation of the Inverse Participation Ratio($IPR$) and it scaling which provides the fractal dimension $D_{2}$. We show that the edge states which exist at the Dirac point of ballistic graphene (no disorder) with zig-zag edges survive in the presence of weak disorder with wavefunctions localized at the boundaries of the flakes. We argue, that there is a strong interplay between the underlying destructive interference mechanism of the honeycomb lattice of graphene leading to edge states and the diffusive interference mechanism introduced by the short-range disorder. This interplay results in a highly abnormal behavior, wavefunctions are becoming progressively less localized as the disorder is increased, indicated by the decrease of the average $\langle IPR\rangle$ and the increase of $D_{2}$. We verify, that this abnormal behavior is absent for graphene flakes with armchair edges which do not provide edge states.