Electronic structure and topological phases of the magnetic layered materials MnBi2Te4, MnBi2Se4, and MnSb2Te4

First-principles calculations are performed to study the electronic structures and topological phases of magnetic layered materials ${\mathrm{MnBi}}_{2}{\mathrm{Te}}_{4}, {\mathrm{MnBi}}_{2}{\mathrm{Se}}_{4}$, and ${\mathrm{MnSb}}_{2}{\mathrm{Te}}_{4}$ under different film thicknesses, strains, and spin-orbit coupling (SOC) strengths. All these compounds energetically prefer the antiferromagnetic (AFM) state. ${\mathrm{MnBi}}_{2}{\mathrm{Te}}_{4}$ and ${\mathrm{MnSb}}_{2}{\mathrm{Te}}_{4}$ bulks are AFM topological insulators (TIs) in the AFM state, while they become Weyl semimetals in the ferromagnetic (FM) state. ${\mathrm{MnBi}}_{2}{\mathrm{Se}}_{4}$ is trivially insulating in both the AFM and FM states, but it becomes an AFM TI or a Weyl semimetal with increasing SOC strength or applying compressive strains. Under equilibrium lattice constants, the FM ${\mathrm{MnBi}}_{2}{\mathrm{Te}}_{4}$ slabs thicker than two septuple layers (SLs), the AFM ${\mathrm{MnBi}}_{2}{\mathrm{Te}}_{4}$ slabs thicker than three SLs, and the FM ${\mathrm{MnSb}}_{2}{\mathrm{Te}}_{4}$ slabs thicker than five SLs are all Chern insulators. In addition, Chern insulators can also be obtained by compressing the in-plane lattice constants of the FM ${\mathrm{MnBi}}_{2}{\mathrm{Se}}_{4}$ slabs thicker than four SLs and the FM ${\mathrm{MnSb}}_{2}{\mathrm{Te}}_{4}$ slabs of three or four SLs, but cannot be obtained using the same method in the AFM slabs of these two materials. In-plane tensile strains about 1% to 2% turn the Chern insulators into trivial insulators.