Figure 1:
A magnetoelectric effect in a topological insulator. (Left) A quantum Hall effect occurs without strong magnetic field when an electric field applied in the plane of the interface between a topological (red region) and an ordinary (blue region) insulator (or vacuum) induces a precisely quantized current perpendicular to the field. (Right) A magnetic field applied perpendicular to the same interface introduces (n+1/2) electrons for each flux quantum of applied field. The shaded region corresponds to the charge density, ρ, of the electrons, which mainly concentrates around the boundary between the two insulators and is largest where the magnetic field is strongest.