▎ 摘　　要

Randomly distributed heavy adatoms on a graphene sheet can effectively enhance local spin-orbit coupling (SOC), hereafter referred to as the SOC impurity. To perform a numerically exact solution of the real-space Kubo-Bastin formula, we study the quantum transport properties of a graphene sheet in the presence of an SOC impurity. We find that the SOC impurity can establish an imperfect quantum spin Hall (QSH) plateau in the band gap region, while nonzero spin Hall conductivity occurs in bulk band regions. In the presence of a magnetic field, the QSH plateau remains in the band gap, accompanying nonzero diagonal spin conductivity and half-integer quantum Hall conductivity outside the band gap. All these features arise from the dual role of the SOC impurity. On the one hand, it acts as a driving force to the QSH state. On the other hand, it is a special scatterer to affect the electronic transport properties in graphene.