Engineering an axion insulator phase in superlattices without inversion symmetry*

We study the interplay between magnetism and topology in three-dimensional HgTe/MnTe superlattices stacked along the (001) axis. Our results show the evolution of the magnetic topological phases with respect to the magnetic configurations. An axion insulator phase is observed for the antiferromagnetic order with out-of-plane magnetization direction below a critical thickness of MnTe, which is the ground state amongst all magnetic configurations.  The axion insulator phase evolves into a trivial insulator as we increase the thickness of the magnetic layers. By switching the magnetization direction into the $ab$ plane, the system realizes different  antiferromagnetic topological insulators depending on the thickness of MnTe.

These phases feature gapless surface Dirac cones shifted away from high-symmetry points.  In the presence of ferromagnetism, the system realizes a magnetic Weyl semimetal and a ferromagnetic semimetal for out-of-plane and in-plane magnetization directions, respectively. We observe large anomalous Hall conductivity in the presence of ferromagnetism in the three-dimensional superlattice.