in a specific [*’segregation’*]{} of the vacancy concentration and self-healing of the graphene.'
author:
- 'E. Nahkmedov$^{1,2}$, E. Nadimi$^{3}$, S. Vedaei$^{3}$, O. Alekperov$^{2}$, F. Tatardar$^{2,4}$, A. I. Najafov$^{2}$, I. I. Abbasov$^{5}$, and A. M. Saletskii$^{6}$'
title: Vacancy mediated magnetization and healing of a graphene monolayer
---

Introduction
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Investigation of graphene, the single two-dimensional (2D) sheet of graphite, is one of the priority direction among of allotropic modifications of carbon and related nanostructures due to its topological properties. Unusual properties of pristine graphene such as ballistic electron propagation with extremely high carrier mobility of $\mu_e=10^4~cm^2V^{-1}s^{-1}$ at room temperature [@ngm04; @geim09], existence of massless, chiral low-energy excitations, characteristic to Dirac fermions, observation of anomalous integer quantum Hall effect (IQHE) even at room temperature [@njzm07], makes it an attractive material for electro-technical industry. Recent experimental and theoretical investigations show that a graphene sheet with vacancies heal themself under thermal annealing or electric potential spanning [@wrgg09; @zzly15; @zbrn12; @rzbb12; @sl01; @zrbn12; @cscx13; @glin10; @wycd12; @spb13; @bpag16; @llly14; @ogc13], so that the vacancies either migrate toward the crystal edge or form a big hole near extended defects like grain boundary or dislocation in the crystal. This property of the graphene may have a great 