A guide to the design of electronic properties of graphene nanoribbons

Graphene nanoribbons (GNRs) are one-dimensional nanostructures predicted to display a rich variety of electronic behaviors. Depending on their structure, GNRs realize metallic and semiconducting electronic structures with band gaps that can be tuned across broad ranges. Certain GNRs also exhibit a peculiar gapped magnetic phase for which the half-metallic state can be induced as well as the topologically nontrivial quantum spin Hall electronic phase. Because their electronic properties are highly tunable, GNRs have quickly become a popular subject of research toward the design of graphene-based nanostructures for technological applications. This Account presents a pedagogical overview of the various degrees of freedom in the atomic structure and interactions that researchers can use to tailor the electronic structure of these materials. The Account provides a broad picture of relevant physical concepts that would facilitate the rational design of GNRs with desired electronic properties through synthetic techniques. We start by discussing a generic model of zigzag GNR within the tight-binding model framework. We then explain how different modifications and extensions of the basic model affect the electronic band structures of GNRs. We classify the modifications based on the following categories: (1) electron-electron and spin-orbit interactions, (2) GNR configuration, which includes width and the crystallographic orientation of the nanoribbon (chirality), and (3) the local structure of the edge. We subdivide this last category into two groups: the effects of the termination of the π-electron system and the variations of electrostatic potential at the edge. This overview of the structure-property relationships provides a view of the many different electronic properties that GNRs can realize. The second part of this Account reviews three recent experimental methods for the synthesis of structurally well-defined GNRs. We describe a family of techniques that use patterning and etching of graphene and graphite to produce GNRs. Chemical unzipping of carbon nanotubes also provides a route toward producing chiral GNRs with atomically smooth edges. Scanning tunneling microscopy/spectroscopy investigations of these unzipped GNRs have revealed edge states and strongly suggest that these GNRs are magnetic. The third approach exploits the surface-assisted self-assembly of GNRs from molecular precursors. This powerful method can provide full control over the atomic structure of narrow nanoribbons and could eventually produce more complex graphene nanostructures.