  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. Indeed, even in the situations where simple
single-electron calculations predict a metallic dispersion, the system is
unstable with respect to the deformation of the carbon-carbon bonds dangling at
the edges of the armchair nanoribbon. The edge bonds' deformation couples
electron and hole states with equal momentum. This coupling opens a gap at the
Fermi level. In a realistic sample, however, it is unlikely that this
instability could be observed in its pure form. Namely, since chemical
properties of the dangling carbon atoms are different from chemical properties
of the atoms inside the sample (for example, the atoms at the edge have only
two neighbours, besides additional non-carbon atoms might be attached to
passivate unpaired covalent carbon bonds), it is very probable that the bonds
at the edge are deformed due to chemical interactions. This chemically-induced
modification of the nanoribbon's edges can be viewed as an effective field
biasing our predicted instability in a particular direction. Yet by disordering
this field (e.g., through random substitution of the radicals attached to the
edges) we may tune the system back to the critical regime and vary the
electronic properties of the system. For example, we show that electrical
transport through a nanoribbon is strongly affected by such disorder.

Mesoscale and Nanoscale Physics;Disordered Systems and Neural Networks