Electronic properties of one-dimensional graphene bilayer ribbons*

The electronic properties of armchair and zigzag bilayer graphene nanoribbons are studied using \textit{ab-initio} density functional theory. We study the effect of width and the electric fields (upto the dielectric breakdown field of SiO2) on their energy gaps [Sahu 2007]. We find metallic and semiconductor arm-chair ribbons and electric field has the effect of increasing the gap in metallic ribbons. The zigzag ribbons due to the edge magnetism show opposite behavior: gap decreases with increase in the applied electric field. We studied small ribbons (below 1 nm) as well as large ribbons (5 nm). In small width arm-chair semiconductor ribbons, the gap decreases whereas in the large width ribbons, the gap increases with applied electric field. Sahu B, Min H, MacDonald AH, and Banerjee SK ``Electronic properties of one-dimensional graphene bilayer ribbons'' (Submitted to Physical Review B).