Effect of interactions on the conductance of graphene nanoribbons

We study the effects of the interaction between electrons and holes on the conductance G of quasi-one-dimensional graphene systems. We first consider as a benchmark the limit in which all interactions are negligible, recovering the predictions of the tight-binding approximation for the spectrum of the system, and the well-known result G=4 e2 /h for the lowest conductance quantum. Then we consider an exactly solvable field theoretical model in which the electromagnetic interactions are effectively local. Finally, we use the effective-field theory formalism to develop an exactly solvable model in which we also include the effect of nonlocal interactions. We find that such interactions turn the nominally metallic armchair graphene nanoribbon into a semiconductor while the short-range interactions lead to a correction to the G=4 e2 /h formula.