The stability of graphene based M\"obius strip with vacancy at high temperature.

By using the density functional theory (DFT) combined with the molecular dynamics (MD) simulations, structural and electronic properties of mono-vacancy (MV) defect in M\"obius strip formed from graphene are investigated. Two kinds of MV are observed depending on the local structures around defects. At static condition, in the curved areas of M\"obius strip, MV has the configuration of one pentagon and one nonagon ring (59-type), which is similar to that of carbon nanotubes and graphene. the most stable MV appear in the twisted areas and has a profile of two pentagon and two hexagon rings (5566-type) with one sp3 hybridized carbon at the central site. While DFT-MD simulations prove that the 5566-type MV is an unstable configuration at room temperature and will transform into a 59-type MV. Additionally, the melting behavior of graphene based M\"obius strips are investigated through empirical potential MD simulations, and we find that their melting temperature is about 2750 K, which is lower than that of carbon nanotubes and graphene.