Systematic study on stanene bulk states and the edge states of its zigzag nanoribbon

Stanene, as a counterpart of graphene, but with much larger spin-orbit coupling (SOC) strength, has recently been synthesized experimentally. Based on first principle calculations and an effective model, we systematically study the electronic and topological properties of bulk stanene under vertical electric field and biaxial strain, which can be naturally introduced by substrates. We find that a topological nontrivial-trivial transition occurs under a critical vertical electric field and an insulator-metal transition happens under critical biaxial strains. We also systematically study the edge state of zigzag nanoribbons. We find that the topological edge state has strong nonlinear dispersion that is different from the previous oversimplified tight-binding (TB) model. A much more practical TB model is built, which captures the strongly nonlinear dispersion of the edge states very well. We investigate four magnetic configurations of the zigzag ribbon edge states in detail and find that the emergence of magnetism for the edge atoms and the magnetization direction have a remarkable impact on the spin-current-carrying edge channels. Furthermore, a half-metallic state can be induced in stanene nanoribbons by applying a transverse electric field, and opposite spin channels can be chosen by reversing the electric field direction. Our results are instructive for future research and applications on stanene and other related buckled systems.