Topological phase transition controlled by electric field in two-dimensional ferromagnetic semiconductors

To tune topological and magnetic properties of systems with band engineering by applying an electric field is of vital important both in physics and in practical applications. In this work, we find a topological phase transition from topologically trivial to nontrivial states at an external electric field of about 0.1 V/\AA\ in ferromagnetic semiconductor MnBi$_2$Te$_4$ monolayer. It is shown that when electric field increases from 0 to 0.15 V/\AA, the magnetic anisotropy energy (MAE) increases from 0.1 meV to about 5 meV, and the Curie temperature Tc increases from 20 to about 70 K. The increased MAE mainly comes from the enhanced spin-orbit coupling due to the applied electric field. The enhanced Tc can be understood from the enhanced $p$-$d$ hybridization and decreased energy difference between $p$ orbitals of Te atoms and $d$ orbitals of Mn atoms. Moreover, we propose two novel Janus materials MnBi$_2$Se$_2$Te$_2$ and MnBi$_2$S$_2$Te$_2$ monolayers with different internal electric polarizations, which can realize quantum anomalous Hall effect (QAHE) with Chern numbers $C$=1 and $C$=2, respectively. Our study not only exposes the electric field induced exotic properties of MnBi$_2$Te$_4$ monolayer, but also proposes novel materials to realize QAHE in ferromagnetic Janus semiconductors with electric polarization.