Zigzag-Shaped Graphene Nanoribbons
This Demonstration presents the atomic structure of superlattices based on graphene nanoribbons. All the structures have the same wiggly shape but different connections of edges.
The unit cell of a zigzag-shaped graphene nanoribbon is described by these three lattice vectors of the honeycomb graphene lattice:
where , and are elementary lattice vectors and , and are integers [1, 2].
The crystallographic orientation of the elementary vectors and defines the ribbon edges to be of type zigzag () or armchair (). The apex angle is the angle between vectors and . The edge type and the apex angle are used for classifying the wiggly structures. The snapshots present the four types of zigzag-shaped graphene nanoribbons.
Snapshot 1: zigzag edges with an apex angle of ()
Snapshot 3: armchair edges with an apex angle of ()
Snapshot 4: armchair edges with an apex angle of ()
The crystallographic orientation of the third elementary vector determines the width ratio between the two fragments of the zigzag-shaped ribbon. The widths of fragments built on the vectors , and , are meant to be measured perpendicular to the vectors and . The width ratio is set to unity in this Demonstration, though a more generic case can also be considered .
The integers , and specify the length and the width of the zigzag-shaped ribbon unit cell. The whole ribbon is obtained by repeated translation of the unit cell by . In this Demonstration, only a few unit cells are shown for clarity.
A similar approach to the classification and atomic position generation can be applied to other two-dimensional crystalline structures, for example, silicene quantum dots .
The atomic coordinates generated in this Demonstration can be used for calculating physical properties of zigzag-shaped ribbons, for example, their electronic properties [1, 2]. The optical properties of these structures can be calculated as described for zigzag ribbons with straight edges .
Graphene nanoribbons very close in shape to those presented here have been produced by the self-assembling of subtly engineered organic molecular precursors .
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