Topological magnetoelectric effect: Coulomb interaction and staggered magnetization

We present theoretical results on the topological magnetoelectric effect (TME) in 3D topological insulators (TIs) with induced magnetization at the surface. We examine the effect of (i) Coulomb interaction among the topological surface states and (ii) a staggered magnetization.
If Coulomb interaction is included, the TME develops a non-local contribution, which can be expressed as an effective topological dipole-dipole interaction between magnetic moments. We discuss the differences compared to the classical dipolar interaction.
If the induced magnetization exhibits staggering, e.g. in a TI bilayer structure with a ferrimagnet or antiferromagnet, the TME causes a coupling of the electric field to the staggered field. In ferrimagnets, the coupling to the staggered field can exceed the coupling to the net magnetization, thus turning the overall response to a topological staggered-field-electric effect (TSE).
References: PRB 93, 014404; PRB 94, 020404; PRB 95, 155430