Graphene nanoribbons are a particularly interesting form of graphene. They have an energy band gap, whereas graphene does not, and their edges impart characteristics not seen in sheet graphene, such as magnetism. Xianlong Wang, Zhi Zeng and colleagues at the Institute of Solid State Physics in Hefei, China, have now calculated how the properties of a graphene nanoribbon change when it is twisted into a Möbius strip with just one edge.1

Fig. 1: A graphene nanoribbon can be folded back onto itself to form a cylinder (top). If it is twisted before folding, it forms a Möbius strip (bottom) with a single continuous edge. The planar triangular region in which stress is concentrated is shown in red. © 2010 AIP

A ribbon can be constructed to have only one edge by twisting so that its ends are joined together to form a Möbius strip (see image). Zeng’s group characterized graphene Möbius strips as a function of their width-to-length ratio using first-principles calculations. They found that as the width-to-length ratio of the graphene Möbius strip increases, a planar triangular region develops and grows in size. At sufficiently high aspect ratios, the strain that develops at the apexes of the triangle is large enough to make the Möbius strip unstable, rendering its fabrication infeasible.

The graphene Möbius strips also have unusual magnetic properties. It is known that graphene nanoribbons with a ‘zigzag’ edge structure exhibit magnetism at their edges. However, the most stable configuration of these ribbons is anti-ferromagnetic, so that magnetic moments at opposite edges point in opposite directions, reducing the total magnetic moment of the ribbons to zero.

In a graphene Möbius strip, however, there can be no magnetic cancellation between the opposite edges because there is only one continuous edge. As a result, graphene Möbius strips have a non-zero magnetic moment. Calculations by Zeng’s group show that this magnetic moment increases with the width-to-length ratio up to a ratio of about 4:10, after which the magnetic moment plateaus and then decreases.

This stable magnetism suggests that spin-polarized transport may be achieved in graphene Möbius strips, with potential applications in spintronic devices. More generally, says Zeng, the Möbius geometry brings a new and interesting set of characteristics to this well-studied material. “Möbius strips constructed from graphene acquire not only the excellent properties of graphene but also special topological properties with potential relevance to microelectronics and other applications.”