Backscattering induced by vacancies in the topological insulator phase of graphene

Theory predicts that the spin orbit interaction (SOI) can turn graphene into a topological insulator. The SOI induces hopping processes between distant carbon atoms giving origin to the quantum spin Hall (QSH) effect, where the bulk sample is insulating and the electronic current that flows only along the system edges is robust against nonmagnetic disorder. Although vacancies are usually treated as a nonmagnetic disorder source, theoretical studies and experimental evidence show evidence of magnetic defects induced by vacancies in graphene. Thus, vacancies are likely to destroy the conductance quantization in the QSH phase by acting as magnetic defects and backscattering the helical edge states. We investigate the electronic transport of graphene in the QSH phase in the presence of those magnetic vacancies. We use an unrestricted Hubbard mean field Hamiltonian to model the electron-electron interaction, which enables both out-of-plane and in-plane magnetization. The last is responsible for spin-flip processes. We use a self-consistent recursive Green's functions technique to calculate the transport quantities and to understand the role of magnetization due to vacancies in the electronic propagation.