Theory of inversion-$\mathbb{Z}_{4}$ protected topological chiral hinge states and its applications to layered antiferromagnets

TL;DR

This paper analyzes the placement of chiral hinge states in higher-order topological insulators with inversion symmetry, revealing how surface orientations and layer parity influence their configurations and topological properties.

Contribution

It exhaustively classifies hinge state configurations in all type-I magnetic space groups with inversion symmetry and applies the findings to layered antiferromagnets, highlighting the effects of layer parity.

Findings

Hinge states depend on surface orientation and symmetry.

Layer parity affects inversion symmetry of hinge states.

Bulk topology determines inversion-asymmetric hinge configurations.

Abstract

We study positions of chiral hinge states in higher-order topological insulators (HOTIs) with inversion symmetry. First, we exhaust all possible configurations of the hinge states in the HOTIs in all type-I magnetic space groups with inversion symmetry by studying dependence of the sign of the surface Dirac mass on surface orientations. In particular, in the presence of glide symmetry, for particular surface orientations, the surface Dirac mass changes sign by changing the surface terminations. By applying this result to a layered antiferromagnet (AFM), we find a difference in the hinge states between the cases with an even and odd number of 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. We show that their inversion-asymmetric configurations are uniquely determined from the symmetries and the topological invariant.