Edge states versus diffusion in disordered graphene flakes

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.