Topological phases in Iridium oxide superlattices: quantized anomalous charge or valley Hall insulators

We study topological phases in Iridium (Ir) oxide superlattices of orthorhombic perovskite-type grown along the [001] crystallographic axis. Due to strong spin-orbit coupling of Ir 5d-orbitals and electronic correlation effects, Ir oxide bilayer superlattices display topological magnetic insulators exhibiting quantized anomalous Hall effects. Depending on stacking of two layers, we also found a valley Hall insulator with counter-propagating edge currents from two different valleys and a topological crystalline insulator with edge states protected by the crystal lattice symmetry. In a single layer Ir oxide superlattice, a topological insulator can be achieved, when a strain field is applied to break the symmetry of a glide plane protecting the Dirac points. In the presence of a magnetic ordering or in-plane magnetic field, it turns into a topological magnetic insulator. We discuss essential ingredients for these topological phases and experimental signatures to test our theoretical proposals.