Sublattice imbalance of states in graphene nanoflakes

Abstract

The energy states of π-electrons in a graphene nanoflake obtained from graphene, a well-known bipartite lattice or honeycomb lattice of carbon atoms, are studied using the tight-binding method. It is reported that the sublattice imbalance ΔN of the entire graphene nanoflake including vacancy clusters, which characterizes the electronic states, consists of those of the outer and inner edges. In nonzero-energy states, the electrons are evenly distributed between the sublattices A and B, regardless of the value of ΔN. In contrast, zero-energy states are ∣ΔN∣-fold degenerate states where the electrons are unevenly distributed on either sublattice A or sublattice B. Occasionally, large or specific graphene nanoflakes have substantial zero-energy states, which are mixed states of the nonzero-energy states and zero-energy states.