Identifying Two-Dimensional Z 2 Antiferromagnetic Topological Insulators

We revisit the question of whether a two-dimensional topological insulator may arise in a commensurate N,el antiferromagnet, where staggered magnetization breaks the symmetry with respect to both elementary translation and time reversal, but retains their product as a symmetry. In contrast to the so-called Z (2) topological insulators, an exhaustive characterization of antiferromagnetic topological phases with the help of topological invariants has been missing. We analyze a simple model of an antiferromagnetic topological insulator and chart its phase diagram, using a recently proposed criterion for centrosymmetric systems [13]. We then adapt two methods, originally designed for paramagnetic systems, and make antiferromagnetic topological phases manifest. The proposed methods apply far beyond the particular examples treated in this work, and admit straightforward generalization. We illustrate this by two examples of non-centrosymmetric systems, where no simple criteria have been known to identify topological phases. We also present, for some cases, an explicit construction of edge states in an antiferromagnetic topological insulator.