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Article Abstract
Graphene antidot lattices (GALs) have garnered significant attention for their potential in semiconductor applications, yet the origin of bandgap opening remains controversial. Combining the octet rule, we propose a low-parameter physical model with weighted information entropy to quantitatively determine the electron density distribution, and the tight-binding parameters are obtained from the occupancy numbers based on the maximum entropy method. The results from our model reveal a complex bandgap opening mechanism in zigzag-edged hexagonal GALs (ZH-GALs), where specific inter-ribbon connections and quantum confinement cause the localization of π-electrons between antidots, leading to the elimination of energy levels degeneracy. We also observe that the anisotropy of rectangular ZH-GALs is enhanced as the defect radius increases, indicating a transition from GALs-like to graphene nanoribbons-like bandgap behavior. This study tells us that more than 1/9 ZH-GALs have considerable bandgaps, addressing the deficiency in band structure engineering between regimes dominated by defect scattering and quantum confinement.
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