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Triangle defect states of hexagonal boron nitride (h-BN) atomic layer were studied by a density functional theory calculation. N(B) triangle defect states of h-BN atomic layer with N(B) edge atoms have acceptor (donor) levels. A cohesive energy calculation indicates that the h-BN atomic layer with N triangle defects is more or less stable, respectively, than that with B triangle defects when it is negatively or positively charged, which is consistent with the recent experimental observation of N triangle defects in h-BN atomic layer. Charge population analysis shows that the edge N(B) atoms surrounding the N(B) triangle defect are negatively (positively) charged. Such a charged triangle defects in h-BN may serve as a potential nanolens for electron-beam focusing.

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