Edge states and sublattice imbalance of rectangular graphene nanoflakes

Abstract

Abstract The energy states of π-electrons in a rectangular graphene flake with a pair of zigzag edges and a pair of armchair edges were studied using a tight-binding method. It is demonstrated that the known exact solution can be interpreted as the results derived from the analytical solutions for graphene nanoribbons on a brick-type lattice by considering the wavefunctions and sublattice imbalance. Edge states in rectangular graphene flakes with a symmetric structure, whose energies are not exactly zero but approach zero as the size increases, are characterized by discrete allowed modes, whereas the zero-energy state appears in rectangular graphene flakes with an asymmetric structure. By applying the edges states of rectangular graphene flakes, zero-energy states were examined in Y-shaped graphene flakes, which involve the same three zigzag edges as in the triangular graphene flakes. Sublattice imbalance in the model was found to force the edge states, including the undamped mode, into zero energy. Configurations of the allowed modes in the zero-energy state are revealed.