More π electrons make a difference: Emergence of many radicals on graphene nanoribbons studied by Ab initio DMRG theory

Graphene nanoribbons (GNRs), also seen as rectangular polycyclic aromatic hydrocarbons, have been intensively studied to explore their potential applicability as superior organic semiconductors with high mobility. The difficulty arises in the synthesis or isolation of GNRs with increased conjugate length, GNRs being known to have radical electrons on their zigzag edges. Here, we use a most advanced ab initio theory based on density matrix renormalization group (DMRG) theory to show the emerging process of how GNRs develop electronic states from nonradical to radical characters with increasing ribbon length. We show the mesoscopic size effect that comes into play in quantum many-body interactions of π electrons, which is responsible for the polyradical nature. An analytic form is presented to model the size dependence of the number of radicals for arbitrary-length GNRs. These results and associated insights deepen the understanding of carbon-based chemistry and offer useful information for the synthesis and design of stable and functional GNRs.