Topological properties of Xene tuned by perpendicular electric field and exchange field in the presence of Rashba spin–orbit coupling

Xene (X=Si, Ge, Sn) is a typical and promising two-dimensional topological insulator with many novel topological properties. Here, we investigate the topological properties of Xene tuned by a perpendicularly applied electric field, exchange field, and Rashba spin–orbit coupling (RSOC) using the tight-binding (TB) method. We show that in the presence of RSOC, the system can be converted from a quantum spin Hall (QSH) insulator into a conventional band insulator (BI) by a weak perpendicular electric field or into a quantum anomalous Hall (QAH) insulator by a weak exchange field. Additionally, a suitable combination of electric and exchange fields can give rise to a valley-polarized metallic (VPM) state. Furthermore, we explore the competition between the electric field and exchange field in tuning the topological states owing to the Rashba coupling effect. When the electric field is stronger than the exchange field, the system tends to be in a topologically trivial BI state; otherwise, it will be a QAH insulator. More intriguingly, for a fixed exchange field and RSOC, as the perpendicular electric field increase continuously from zero, the system undergoes multiphase (e.g. QSH-VPM-BI) transitions. This paves the way for designing multiphase transition devices through external single-field regulation.