Abstract
We investigate the properties of a graphene system taking into account both the on-site Coulomb repulsion and the Rashba spin-orbit coupling caused by a transverse electric field by using a mean-field approximation of the Hubbard model. It is found that by increasing the strength of the Rashba spin-orbit coupling, the system with a strong Coulomb interaction can successively go through three phases: valley polarized insulator, valley polarized metal, and normal metal, in which the first two phases are new ones characterized by their specific band structures. Hence, a valley polarized insulator-metal phase transition can occur by changing the strength of the spin-orbit coupling in this system. We propose a mechanism of valley filter based on the gated valley polarized insulator, in which a net K or K′ valley current can be obtained.
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