Strain control of band topology and surface states in antiferromagnetic ${\mathrm{EuCd}}_2{\mathrm{As}}_2$

Topological semimetal antiferromagnets provide a rich source of exotic topological states which can be controlled by manipulating the orientation of the Néel vector, or by modulating the lattice parameters through strain. We investigate via ab initio density functional theory calculations, the effects of shear strain on the bulk and surface states in two antiferromagnetic ${\mathrm{EuCd}}_2{\mathrm{As}}_2$ phases with out-of-plane and in-plane spin configurations. When magnetic moments are along the $c$ axis, a 3% longitudinal or diagonal shear strain can tune the Dirac semimetal phase to an axion insulator phase, characterized by the parity-based invariant ${\eta }_{4I}=2$. For an in-plane magnetic order, the axion insulator phase remains robust under all shear strains. We further find that for both magnetic orders, the bulk gap increases, and a surface gap opens on the (001) surface up to 16 meV. Because of a nonzero ${\eta }_{4I}$ index and gapped states on the (001) surface, hinge modes are expected to happen on the side surface states between those gapped surface states. This result can provide valuable insight into the realization of the long-sought axion states.