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arXiv · 1303.3488

Edge states versus diffusion in disordered graphene flakes

Ioannis Kleftogiannis·Ilias Amanatidis
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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.

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Ioannis Kleftogiannis, Ilias Amanatidis. 2014-02-20. Edge states versus diffusion in disordered graphene flakes. https://doi.org/10.1140/epjb%2Fe2013-40756-0

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