Engineering axion insulator and other topological phases in superlattices without inversion symmetry

We study theoretically the interplay between magnetism and topology in three-dimensional HgTe/MnTe superlattices stacked along (001) axis. Our results show evolution of magnetic topological phases with respect to configurations. An axion insulator phase is observed for antiferromagnetic order out-of-plane N\'eel vector direction below a critical thickness MnTe, which ground state amongst all Defining $T$ as time-reversal symmetry, this protected by two-fold rotational symmetry $C_2{\cdot}T$. The evolves into trivial we increase layers. By switching $ab$ plane, system realizes different insulators depending on MnTe. These feature gapless surface Dirac cones shifted away from high-symmetry points surfaces perpendicular In presence ferromagnetism, Weyl semimetal ferromagnetic in-plane magnetization directions, respectively. observe large anomalous Hall conductivity ferromagnetism superlattice.