  First-principles calculations are performed to study the electronic
structures and topological phases of magnetic layered materials MnBi2Te4,
MnBi2Se4 and MnSb2Te4 under different film thicknesses, strains and spin-orbit
coupling (SOC) strengths. All these compounds energetically prefer the
antiferromagnetic (AFM) state. MnBi2Te4 and MnSb2Te4 bulks are AFM topological
insulators (TIs) in the AFM state, while they become Weyl semimetals in the
ferromagnetic (FM) state. MnBi2Se4 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 MnBi2Te4 slabs thicker than two septuple layers (SLs), the AFM MnBi2Te4
slabs thicker than three SLs and the FM MnSb2Te4 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 MnBi2Se4 slabs thicker
than four SLs and the FM MnSb2Te4 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.
