Spin-charge order and excitonic effects in sawtooth-like graphene nanoribbons

•The band gap is not monotonically decreasing but exhibits a oscillation.•A variety of magnetic orders root in the competition of the short range and long range exchange interaction.•The charge distributions of excitons are related to the spin-resolved charge density distributions in the ground state.•The interaction between electrons and holes in degenerate spin-triplets T1T1 and T−1T−1 is stronger than that for T0T0.

In this paper we systematically study electronic structures and excitonic effects in one type of the sawtooth-like graphene nanoribbons. A main feature is that the local magnetism is developed for the certain width and changes with the increase of width. A variety of magnetic orders root in the competition of the short range interaction between the same spin-electrons and long range exchange interaction between opposite spin-electrons. For excitonic effects, the binding energy of degenerate spin-triplets T1T1 and T−1T−1 is higher than that of T0T0 for all studied nanoribbons and is size dependent. We reveal the underlying physical mechanism from the charge distributions of excitons and its correlation with the spin-resolved charge density distributions in the ground state. We find that the electrons and holes in degenerate spin-triplets T1T1 and T−1T−1 are closer together and thus the interaction between them is more strong, while the distribution of electrons and holes is relatively more disperse for T0T0, indicating the weaker interaction. We hope that these interesting results are able to be detected in the experiment and these multi-performance samples are better utilized in future device applications.