Magnetoelectric polarizability and axion electrodynamics in crystalline insulators

TL;DR

The orbital motion of electrons in a three-dimensional solid can generate a pseudoscalar magnetoelectric coupling theta, a fact that can be generalized to the many-particle wave function and defines the 3D topological insulator in terms of a topological ground-state response function.

Abstract

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 $Δ{\cal L}_{EM} = (θe^2 / 2 πh) {\bf E} \cdot {\bf B}$, 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 wavefunction and defines the 3D topological insulator, like the IQHE, in terms of a topological ground-state response function.

Figures (2)

• Figure 1: The magnetoelectric polarizability $\theta$ (in units of $e^2/2\pi h$). The filled squares are computed by the Chern-Simons form, Eq. (\ref{['theta']}). The open squares are $dP/dB$ from Eq. (\ref{['polarization']}). The points are obtained by layer-resolved $\sigma_\mathrm{H}$ calculations using Eq. (\ref{['conductance']}). The curve is obtained from Eq. (\ref{['secondchernapp']}).
• Figure 2: (Color online) The layer-resolved Hall conductivity (in units of $e^2/h$) at $\beta = \pi$ in a slab of twenty layers, with $m=t/2$ and $\lambda_{SO} = t/4$, terminated in $(\bar{1}11)$ planes.