Witten effect in a crystalline topological insulator

It has been noted a long time ago that a term of the form θ(e²/2πh)B·E may be added to the standard Maxwell Lagrangian without modifying the familiar laws of electricity and magnetism. θ 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 θ≠0 is predicted to bind a (generally fractional) electric charge -e(θ/2π+n) with n integer. Here we conduct a test of the Witten effect based on the recently established fact that the axion term with θ=π 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.