From aromaticity to self-organized criticality in graphene

The unique properties of graphene are rooted in its peculiar electronic structure where effects of electron delocalization are pivotal. We show that the traditional view of delocalization as formation of a local or global aromatic bonding framework has to be expanded in this case. A modification of the π-electron system of a finite-size graphene substrate results in a scale-invariant response in the relaxation of interatomic distances and reveals self-organized criticality as a mode of delocalized bonding. Graphene is shown to belong to a diverse class of finite-size extended systems with simple local interactions where complexity emerges spontaneously under very general conditions that can be a critical factor controlling observable properties such as chemical activity, electron transport, and spin-polarization.