Electric Polarization and End States in Boron Nitride Nanoribbons*

Using first-principles calculations, we find that armchair BNNRs have an intrinsic electric polarization along the periodic direction for different ribbon widths. Like finite-length armchair graphene nanoribbons, finite-length armchair BNNRs also have end states at their zigzag ends. We are able to classify the end states by applying an electric field to offset the intrinsic polarization in BNNRs. We calculate the Zak phase of armchair BNNRs (whose unit cells do not have inversion or mirror symmetry) as a function of the width of the ribbon. We also study the relation between the Zak phase and the existence of end states.