Excitonic effects of E11, E22, and E33 in armchair-edged graphene nanoribbons

We explore excitonic effects of E11, E22, and E33, which are excitons formed between the three highest valence subbands and the three lowest conduction ones, in armchair-edged graphene nanoribbons by applying the extended tight-binding model including electron-electron interactions. Our results show that the excitation energies and the binding energies decrease inversely with the ribbon widths and can be classified into three categories based on their width indices. We found the relation between the band structures and the binding energies and explained some recent observations of strong excitonic effects in graphene