Competition of edge effects on the electronic properties and excitonic effects in short graphene nanoribbons

We explore the electronic properties and exciton effects in short graphene nanoribbons (SGNRs), which have two armchair edges and two zigzag edges. Our results show that both of these two types of edges have profound effects on the electronic properties and exciton effects. Both the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) states are alternatively changed between the bulk and the edge states as the lengths of the zigzag edges increase, due to the competition between the states of the two types of edges. The energy gaps, as a function of the lengths of the armchair edges, will then induce two kinds of trends. Furthermore, two kinds of exciton energies and exciton binding energies are found, which can be understood through the two kinds of HOMO and LUMO states in SGNRs. In addition, we find that the three triplet exciton states are not totally energy degenerate in SGNRs due to the spin-polarized states on the zigzag edges.