Effect of deformation on the electronic structure and topological properties of the $\mathrm{A^{II}Mg_2Bi_2 \: (A^{II}= Mg, Ca, Sr, Ba)}$ compounds

The electronic structure and topological properties of the $\mathrm{A^{II}Mg_2Bi_2 \: (A^{II}= Mg, Ca, Sr, Ba)}$ compounds are theoretically studied with the use of exact exchange. It is found that the $\mathrm{Mg_3Bi_2}$ compound in the equilibrium state is a semimetal, whereas three other compounds are semiconductors with a direct fundamental band gap. It is predicted that the uniaxial deformation of three-component compounds results in transitions to topologically nontrivial phases: topological insulator and topological and Dirac semimetals. Owing to such a rich variety of topologically nontrivial phases, these compounds may be of interest for further theoretical and experimental studies.