Magnetoelectric polarizability and axion electrodynamics in crystalline insulators

TL;DR

This paper derives the orbital magnetoelectric polarizability parameter θ in crystalline insulators, linking it to axion electrodynamics and topological insulators, and discusses its surface and many-particle properties.

Contribution

It provides a theoretical derivation of the pseudoscalar magnetoelectric coupling θ in crystalline insulators and connects it to topological insulator properties and axion electrodynamics.

Findings

Derived θ for a simple topological insulator model

Connected θ to surface Hall conductivity

Extended the concept to many-particle wavefunctions

Abstract

The orbital motion of electrons in a three-dimensional solid can generate a pseudoscalar magnetoelectric coupling $\theta$, a fact we derive for the single-particle case using a recent theory of polarization in weakly inhomogeneous materials. This polarizability $\theta$ is the same parameter that appears in the "axion electrodynamics" Lagrangian $\Delta{\cal L}_{EM} = (\theta e^2 / 2 \pi h) {\bf E} \cdot {\bf B}$, which is known to describe the unusual magnetoelectric properties of the three-dimensional topological insulator ($\theta=\pi$). We compute $\theta$ 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 wavefunction and defines the 3D topological insulator, like the IQHE, in terms of a topological ground-state response function.