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Vacancy induced zero energy modes in graphene stacks: The case of ABC trilayer

The zero energy modes induced by vacancies in ABC stacked trilayer graphene are investigated. Depending on the position of the vacancy, a new zero energy solution is realised, different from those obtained in multilayer compounds with Bernal stacking. The electronic modification induced in the sample by the new vacancy states is characterised by computing the local density of states and their localisation properties are studied by the inverse participation ratio. We also analyse the situation in the presence of a gap in the spectrum due to a perpendicular electric field.