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Using first-principles density-functional theory, we study the electronicstructure of multilayer graphene nanoribbons as a function of the ribbon widthand the external electric field, applied perpendicular to the ribbon layers. Weconsider two types of edges (armchair and zigzag), each with two edgealignments (referred to as alpha- and beta-alignments). We show that, as inmonolayer and bilayer armchair nanoribbons, multilayer armchair nanoribbonsexhibit three classes of energy gaps which decrease with increasing width.Nonmagnetic multilayer zigzag nanoribbons have band structures that aresensitive to the edge alignments and the number of layers, indicating differentmagnetic properties and resulting energy gaps. We find that energy gaps can beinduced in ABC-stacked ribbons with a perpendicular external electric fieldwhile in other stacking sequences, the gaps decrease or remain closed as theexternal electric field increases.

Effects of edge magnetism and external electric field on energy gaps in multilayer graphene nanoribbons