We study the effect of magnetism and perpendicular external electric field strengths on the energy gap of length confined bilayer graphene nanoribbons (or nanobars) using a first principles density functional electronic structure method and a semi-local exchange-correlation approximation. We assume AB (Bernal) bilayer stacking and consider both armchair and zigzag edges and for each edge type, the two edge alignments, namely, \alpha and \beta edge alignment. We identify three distinct classes of bilayer energy gaps, defined by number of carbon chains in the width direction (N = 3p, 3p+1 and 3p+2, p is an integer), for the armchair nanobars and the gaps decrease with increasing width except for class 3p+2 armchair nanoribbons. Metallic-like behavior seen in armchair bilayer nanoribbons are found to be absent in armchair nanobars. Class 3p+2 armchair nanobars show significant length dependence and their gaps approach those of nanoribbons as length increases. A critical gap seems to occur above and below which the external electric field between the layers shows opposite behavior. Magnetism between the layers plays a major role in enhancing the gap values resulting from the geometrical confinement hinting at an interplay of magnetism and geometrical confinement in finite size bilayer graphene.
Citation: Physical Review B
Pub Type: Journals
Graphene, Electronic structure, Density functional theory