Valley-polarized metals and quantum anomalous Hall effect in silicene

Silicene is a monolayer of silicon atoms forming a two-dimensional honeycomb lattice, which shares almost every remarkable property with graphene. The low-energy structure of silicene is described by Dirac electrons with relatively large spin-orbit interactions due to its buckled structure. The key observation is that the band structure is controllable by applying electric field to silicene. We explore the phase diagram of silicene together with exchange field M and by applying electric field E(z). A quantum anomalous Hall (QAH) insulator, valley polarized metal (VPM), marginal valley polarized metal (M-VPM), quantum spin Hall insulator, and band insulator appear. They are characterized by the Chern numbers and/or by the edge modes of a nanoribbon. It is intriguing that electrons have been moved from a conduction band at the K point to a valence band at the K' point for E(z) > 0 in the VPM. We find in the QAH phase that almost flat gapless edge modes emerge and that spins form a momentum-space Skyrmion to yield the Chern number. It is remarkable that a topological quantum phase transition can be induced simply by changing electric field in a single silicene sheet.