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.

Highlights

  • The discovery of topological insulators (TIs) has triggered intensive studies on topological aspects in electronic structures of solids [1,2]

  • We found all the possible configurations of chiral hinge states (CHSs) in higher-order topological insulators (HOTIs) in type-I magnetic space groups (MSGs) with I symmetry through an analysis of the sign of the surface Dirac mass

  • We found that in systems with glide symmetry, two surface terminations with the same particular surface orientations have the opposite signs of the mass

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Summary

INTRODUCTION

The discovery of topological insulators (TIs) has triggered intensive studies on topological aspects in electronic structures of solids [1,2]. We find all the possible patterns of positions of CHSs in HOTIs from I symmetry. 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, and we find emergence of I-asymmetric hinge states (IAHSs) in the case of an even number of layers. We show that IAHSs result from the bulk Z4 topology protected by I symmetry, and they generally appear in antiferromagnets (AFMs) with an even number of layers and the nontrivial Z4 index.

TYPE-I MAGNETIC SPACE GROUPS WITH INVERSION SYMMETRY
CHIRAL HINGE STATES IN ANTIFERROMAGNETIC HIGHER-ORDER TOPOLOGICAL INSULATORS
Cases with an odd number of layers
Cases with an even number of layers
MODEL CALCULATIONS
CONCLUSION
Setup of the problem
Point groups
Screw symmetry
Glide symmetry

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