Hybrid-order topology with tunable chiral hinge modes and unpinned Dirac surface states in the altermagnetic insulator Eu_3In_2As_4

The exploration of magnetic topological states is instrumental in exploring axion electrodynamics and intriguing transport phenomena, such as the quantum anomalous Hall effect. Here, we predict that the recently-synthesized material Eu_3In_2As_4 exhibits as both an axion insulator and a 3D Stiefel-Whitney insulator with an altermagnetic order. When spins align in the ab plane, we find an unpinned surface Dirac cone on the ab plane and chiral hinge states along the c direction, where hinge states can generate a half-quantized surface anomalous Hall effect on the ac and bc facets. When spins align along c, we observe a mirror-protected topological crystalline insulator. Furthermore, the ferromagnetic phase, in which spins are aligned in the same direction by an external in-plane magnetic field, presents an ideal Weyl semimetal with a single pair of type-I Weyl points and no extra Fermi pocket. Our work predicts rich topological states tuned by magnetic structures in Eu_3In_2As_4, supporting the further study of the topological transport and Majorana fermions in proximity to a superconductor.