Magnetoelectric Polarizability and Axion Electrodynamics in Crystalline Insulators

The orbital motion of electrons in a three-dimensional solid can generate a pseudoscalar magnetoelectric coupling θ, a fact we derive for the single-particle case using a recent theory of polarization in weakly inhomogeneous materials. This polarizability θ is the same parameter that appears in the “axion electrodynamics” Lagrangian ∆LEM=(θe2/2πh)E·B, which is known to describe the unusual magnetoelectric properties of the three-dimensional topological insulator (θ=π). We compute θ for a simple model that accesses the topological insulator and discuss its connection to the surface Hall conductivity. The orbital magnetoelectric polarizability can be generalized to the many-particle wave function and defines the 3D topological insulator, like the integer quantum Hall effect, in terms of a topological ground-state response function.