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Theory of inversion-Z_{4} protected topological chiral hinge states and its applications to layered antiferromagnets

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

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