Graphene nanoribbons without cutting graphene*

We show that the 2D periodic graphene deposited on Silicon Carbide surface with a trench mimics a grapheme nanoribbon. Our study is carried out with calculations based on Density Functional Theory. In our work, the graphene is deposited at the [0001] and the [0001 \={ }] surfaces. We investigate the influence of the charge transfer between the graphene and the substrate, the local magnetic moment, as well as the direction of the trench on the electronic properties of such systems. Our results suggest that at the [0001] surface the charge transfer is large resulting in a large change in the Fermi energy. As a consequence, the mimicked armchair graphene nanoribbons turn out to be metallic and the mimicked zigzag graphene nanoribbons are nonmagnetic. These properties are distinct from the corresponding free standing graphene nanoribbons. On the other hand, at the [0001 \={ }] surface, the charge transfer is small, and the properties of the mimicked ribbons are very similar to the free standing ones.