4 tion systems. Our results for vacancies are consistent with the most salient features of the H-dosing-induced MIT in graphene as observed in recent experiments [13], suggesting that both vacancy and H belong to the same class of short-range disorders in graphene with H dos- ing involving stronger multiple scattering. Our studies also shed some new lights to the general understanding of critical behaviors of 2D disordered systems. Fig. 4(b), we plot l as a function of x , which shows that l scales with x in a power law l = Ax δ ( δ = − 0 . 5 ) at E$_{F}$ . Fitting the simulation data, we obtained the parameter A = 0 . 508 nm. This power-law scaling has been derived before from the full self-consistent Born approximation (FSBA) [7], but the FSBA is limited to extremely low concentration and can not describe the localization be- havior near E$_{F}$ and give the quantitative values of l . Our quantitative results indicate that vacancies are short-range disorders similar to H atoms in graphene as suggested by a recent experiment [13]. The similar re- sults between vacancy defect and H impurity can be un- derstood by the dramatic reconstruction of the energy spectrum near the Dirac point in both cases, while the Fermi energy is preserved. As short-range local scatters, both vacancy and H lead to strong localization by sig- nificant scattering. We note that at low defect/impurity concentration, the mean free path l is shorter for vacancy ( 1 . 6 nm at x = 0 . 1% ) than for H atom ( ∼ 4 − 5 nm at x = 0 . 1% ). This is because vacancy produces a much stronger local scattering center (creating an infinite bar- rier) than H (inducing a structural transition from sp 2 to sp 3 hybridization). However, we find that the rate of l decreases faster with x for H ( δ < − 1 ) [13] than that for vacancy ( δ = − 0 . 5 ). This is possibly because the scattering center produced by vacancy is more localized limited to single atomic site, while the scattering center produced by H atom is relatively more extended as the sp 3 hybridization induces reconstruction in the neighbor- ing atoms around it. Consequently, at high concentra- tion, multiple scattering by H atoms becomes more and more important, leading to a faster decay of l . A differ- ent case was shown in graphene substituted with boron or nitrogen, where the long-range scattering is induced by chemical disorder with δ = − 1 [18]. In conclusion, the criticality of vacancy-induced MIT in graphene has been investigated with quantitative sim- ulations. The MIT is shown to occur at the critical va- cancy concentration x$_{c}$ ≈ 0 . 053% , caused by the vacancy- induced quasi -localization. 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