▎ 摘　　要

In this letter, controllable optical bistability (OB) and optical multistability (OM) in a defect slab doped with a single-layer graphene nanostructure are proposed. Our numerical results show that it is easy to control OB by Rabi frequencies of coupling fields, detuning of coherent fields, and relative phase of applied fields. Moreover, the thickness effect of the slab is considered as a new parameter for controlling the OB behaviors. It is found that the transition from OB to OM or vice versa can be made possible by the thickness of the slab and relative phase of the applied fields. We hope that our results will have potential applications in quantum information science and technology based nanoscale devices.