Model Hamiltonian and time reversal breaking topological phases of antiferromagnetic half-Heusler materials

In this work, we construct a generalized Kane model with a coupling term between itinerant electron spins and local magnetic moments of antiferromagnetic ordering in order to describe the low-energy effective physics in a large family of antiferromagnetic half-Heusler materials. The topological properties of this generalized Kane model are studied and a large variety of topological phases, including the Dirac semimetal phase, Weyl semimetal phase, nodal line semimetal phase, type-B triple point semimetal phase, topological mirror (or glide) insulating phase, and antiferromagnetic topological insulating phase, are identified in different parameter regions of our effective models. In particular, we find that the system is always driven into the antiferromagnetic topological insulator phase once a bulk band gap is open, irrespective of the magnetic moment direction, thus providing a robust realization of antiferromagentic topological insulators. Furthermore, we discuss the possible realization of these topological phases in realistic antiferromagnetic half-Heusler materials. Our effective model provides a basis for the future study of physical phenomena in this class of materials.