Witten effect in a crystalline topological insulator

It has been noted a long time ago that a term of the form $\theta \left(e^2/2\pi h\right)\mathbf{B}\cdot \mathbf{E}$ may be added to the standard Maxwell Lagrangian without modifying the familiar laws of electricity and magnetism. $\theta$ is known to particle physicists as the “axion” field and whether or not it has a nonzero expectation value in vacuum remains a fundamental open question of the standard model. A key manifestation of the axion term is the Witten effect: a unit magnetic monopole placed inside a medium with $\theta \ne 0$ is predicted to bind a (generally fractional) electric charge $-e\left(\theta /2\pi +n\right)$ with $n$ integer. Here we conduct a test of the Witten effect based on the recently established fact that the axion term with $\theta =\pi$ emerges naturally in the description of the electromagnetic response of a class of crystalline solids called topological insulators—materials distinguished by strong spin-orbit coupling and nontrivial band structures. Using a simple physical model for a topological insulator we demonstrate the existence of a fractional charge bound to a monopole by an explicit numerical calculation. We also propose a scheme for generating an “artificial” magnetic monopole in a topological insulator film that may be used to facilitate an experimental test of Witten’s prediction.