We studied the electronic structure of Si$_2$Bi$_2$ through a first-principles calculation based on the density functional theory. Si$_2$Bi$_2$, a van der Waals layered structure, which possesses an in-plane $C_3$ rotational and time-reversal symmetries as well as inversion, exhibits metallic characteristics in equilibrium. Intriguingly, its electronic band structure reveals Dirac cones existing near the Fermi level. In addition, we observed that Si$_2$Bi$_2$ could undergo a phase transition from metallic to topological insulating phases due to in-plane compressive strains, either uniaxial or biaxial. In particular, its band structure evolution under the uniaxial compressive strain along the zigzag direction revealed that a band inversion had occurred. Our hybrid Wannier charge center calculation confirmed that this material, indeed, becomes a topological insulator. Finally, we constructed its topological phase diagram in the parameter space of the in-plane strain fields, which revealed how to control the in-plane strain to realize the topologically different phases of Si$_2$Bi$_2$.

Keywords: Layered materials, Density functional theory, Electronic structures, Topological phase transition, In-plane strain