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A flat band in fermionic system is a dispersionless single-particle state with a diverging effective mass and nearly zero group velocity. These flat bands are expected to support exotic properties in the ground state, which might be important for a wide range of promising physical phenomena. For many applications, it is highly desirable to have such states in Dirac materials, but so far they have been reported only in some nonmagnetic Dirac systems. In this paper, we propose a realization of topologically protected spin-polarized flat bands generated by domain walls in planar magnetic topological insulators. Using first-principles material design, we suggest a family of intrinsic antiferromagnetic topological insulators with an in-plane sublattice magnetization and high Néel temperature. Such systems can host domain walls in a natural manner. For these materials, we demonstrate the existence of spin-polarized flat bands in the vicinity of the Fermi level and discuss their properties and potential applications.

We report an ab initio study of the effect of pressure on vibrational and electronic properties of K3Bi and Rb3Bi in the cubic Fm3m structure. It is shown that the high-temperature cubic phase of K3Bi and Rb3Bi is dynamically unstable at T=0 but can be stabilized by pressure. The electronic spectra of alkali bismuthides are found to possess the bulk band touching at the Brillouin zone center and an inverted spin-orbit bulk band structure. Upon hydrostatic compression the compounds transform from the topologically nontrivial semimetal (K3Bi)/metal (Rb3Bi) into a trivial semiconductor (metal) with a conical Dirac-type dispersion of electronic bands at the point of the topological transition. In K3Bi the dynamical stabilization occurs before the system undergoes the topological phase transition.