Direct measurement of the quantized topological magnetoelectric effect
In plain words
An axion insulator should become electrically polarized in a magnetic field by an amount fixed only by the fine-structure constant, and this static effect has never been measured directly.
Precise statement
For an axion insulator with $\theta = \pi$ (magnetic topological insulator sandwich or even-layer MnBi2Te4), measure the static (dc) magnetoelectric response $P = (\theta \alpha / 4\pi^2) B$ in Gaussian units with $\alpha = e^2/(\hbar c)$, i.e., $\alpha/(4\pi)$ per unit field at $\theta = \pi$, or the equivalent magnetization induced by an electric field. An answer is the measured coefficient in units of $\alpha/(4\pi)$ with accuracy better than 10%.
What would settle it
Capacitive or SQUID detection of field-induced polarization, or electric-field-induced magnetization, in an insulating sample free of dissipative edge or side-wall conduction.
Status in the literature
Unverified note
Quantized Faraday and Kerr rotations, a terahertz-frequency form of the effect in an applied field, were reported in topological insulator films in 2016-2017; a static (dc) measurement of $P = (\alpha/4\pi) B$ in an axion insulator is lacking as of 2026.