Finding the $V_2(555 − 777)$ Double Vacancy Defect in Graphene Using Rotational Symmetry

Document Type : Research Paper


1 The John Knopfmacher Centre for Applicable Analysis and Number Theory, School of Mathematics, University of the Witwatersrand, Private Bag 3, P O WITS 2050, South Africa

2 AGH University of Science and Technology, Faculty of Applied Mathematics, al. A. Mickiewicza 30, 30-059 Krakow, Poland


We use the underlying hexagonal structure of graphene to identify uniquely the
position pertaining to a divacancy defect of type $V_2(555 − 777)$. This is achieved by
considering at most three closed path readings and the symmetry of the defective structure. We work in the corresponding rectangular model but still rely on the rotational
symmetry of the original hexagonal grid. Our approach is purely mathematical and
therefore there is no need for imaging technologies.


Main Subjects

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