# Model Hamiltonian and Time Reversal Breaking Topological Phases of Anti-ferromagnetic Half-Heusler Materials

## TL;DR

This paper develops a generalized Kane model to describe various topological phases in anti-ferromagnetic half-Heusler materials, revealing robust anti-ferromagnetic topological insulators and potential for experimental realization.

## Contribution

It introduces a new coupling term in the Kane model to capture anti-ferromagnetic effects and identifies multiple topological phases in these materials.

## Key findings

- Identification of diverse topological phases including Dirac, Weyl, and nodal line semimetals.
- Discovery that the system becomes an anti-ferromagnetic topological insulator when a bulk gap opens.
- The model suggests feasible experimental realization in real materials.

## Abstract

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