Topological and magnetic phase transition in silicene-like zigzag nanoribbons

Spin-orbital interactions (SOI) in silicene results in the quantum-spin-Hall effect, while the Hubbard-induced Coulomb interaction in zigzag nanoribbons often generates a band gap with the anti-ferromagnetic (AF) spin orders on two edges. In this paper we systematically study these two joint contributions to the zigzag silicene-like nanoribbons (zSiNR). Some topological and magnetic phase transitions are investigated with different material parameters and external fields. We find when the ribbon width or the SOI value exceeds some critical value, the SOI may overcome the Coulomb interaction and the system transits from a band insulator to a topological insulator: the quantum-spin-Hall or the spin quantum-anomalous Hall state. We also find some magnetic phase transition exists in the Hubbard-dominated zSiNR systems when the exchange field or the electric field goes beyond some critical values. Lastly we observe a double topological/magnetic phase transition in a Hubbard-SOI-balanced zSiNR system before the magnetic and topological phases are destroyed by a strong electric field.