Electronic properties of armchair graphene nanoribbons

We investigate the electronic band structure of an undoped graphene armchair nanoribbon. We demonstrate that such nanoribbon always has a gap in its electronic spectrum. Even if the parameters of the noninteracting Hamiltonian are fine tuned to a point where single-electron calculations predict a metallic dispersion, the system becomes unstable toward the spontaneous deformation of the carbon-carbon bonds dangling at the edges of the nanoribbon. This deformation produces a spectral gap. However, to directly observe this instability it is necessary to have a precise control over the parameters of the system, which is rarely possible in practice. As a result, the nanoribbon's Hamiltonian deviates from the instability point. This deviation plays the role of an effective external field biasing the instability in a particular direction. Since the radicals passivating the edge affect the dangling bonds, one may vary this field to some extent by choosing different radicals for passivation. Unfortunately, this approach lacks the accuracy required for a thorough cancellation of the effective field. Disordering the effective field is a more convenient tool of controlling the electronic properties. Such disorder can be introduced through random substitution of the radicals passivating the edges by different radicals. We show that disorder could tune a nanoribbon of finite length back to the gapless regime. This would significantly influence the electronic properties of the system. Specifically, we show that the electrical transport through a nanoribbon is strongly affected by edge disorder.