  Tuning topological and magnetic properties of materials by applying an electric field is widely used in spintronics. 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/A in MnBi$_2$Te$_4$ monolayer that is a topologically trivial ferromagnetic semiconductor. It is shown that when electric field increases from 0 to 0.15 V/A, the magnetic anisotropy energy (MAE) increases from about 0.1 to 6.3 meV, and the Curie temperature Tc increases from 13 to about 61 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 MnBi2Te4 monolayer, but also proposes novel materials to realize QAHE in ferromagnetic Janus semiconductors with electric polarization. 
Electric field induced topological phase transition and large   enhancements of spin-orbit coupling and Curie temperature in two-dimensional   ferromagnetic semiconductors