Identifying two-dimensional $Z_2$ antiferromagnetic topological insulators

摘要

We revisit the question of whether a two-dimensional topological insulatormay arise in a commensurate N\'eel antiferromagnet, where staggeredmagnetization breaks both the elementary translation and time reversal, butretains their product as a symmetry. In contrast to the so-called $Z_2$topological insulators, an exhaustive characterization of antiferromagnetictopological phases with the help of a topological invariant has been missing.We analyze a simple model of an antiferromagnetic topological insulator andchart its phase diagram based on a recently proposed criterion forcentrosymmetric systems [Fang et al., Phys. Rev. B 88, 085406 (2013)]. We thenadapt two methods, originally designed for paramagnetic systems, and makeantiferromagnetic topological phases manifest. The proposed methods apply farbeyond the particular example treated in this work, and admit straightforwardgeneralization. We illustrate this by considering a non-centrosymmetric system,where there are no simple criteria to identify topological phases. We alsopresent an explicit construction of edge states in an antiferromagnetictopological insulator.