Topological Inversion-Asymmetric Hinge States Protected by the Intrinsic Inversion Symmetry

Abstract

We propose inversion-asymmetric hinge states, which are different from the conventional inversion-symmetric hinge states in the higher-order topological insulators (HOTIs) realized in layered antiferromagnets (AFMs). First, we find all possible configurations of the hinge states in the HOTIs in all type-I magnetic space groups with inversion symmetry. In particular, in a layered AFM, we find a difference in the hinge states between the cases with an even and odd number of the layers. In the case of an even number of layers, which does not preserve inversion symmetry, positions of hinge states are not inversion symmetric. Nonetheless, these inversion-asymmetric hinge states result from the bulk topology protected by inversion symmetry. We show that their inversion-asymmetric configurations are uniquely determined from the symmetries and the topological invariant.