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Topological insulators (TIs) in three space dimensions can be characterized by a quantized magnetoelectric coefficient. However, this coupling does not have experimentally observable consequences in the presence of time‐reversal symmetry, because the contributions of both bulk and surface states cancel each other. Instead, the characteristic response of a TI is a nonlinear magnetoelectric effect. Field theoretic aspects of the nonlinear magnetoelectric response and numerical calculations for experimentally relevant geometries are discussed. Distinct from this effect, the magnetoelectric coupling would bind a charge ± e /2 in response to a monopole, which is referred to as Witten effect. If time reversal is broken explicitly, for instance, by a Zeeman field acting on the surface layer, the electromagnetic response of a TI can be described by a half‐integer quantum Hall effect of surface electrons.

Topological Magnetoelectric Effect: Nonlinear Time‐Reversal‐Symmetric Response, Witten Effect, and Half‐Integer Quantum Hall Effect