The topological Faraday effect cannot be observed in a realistic sample

TL;DR

The paper argues that observing the topological magneto-electric effect in realistic 3D topological insulator samples via optical methods is fundamentally unfeasible due to non-universal responses caused by material and interface effects.

Contribution

It critically examines the feasibility of detecting the TME effect optically, highlighting the impact of impedance mismatch and bulk carriers on the response.

Findings

Magneto-optical response is non-universal with impedance mismatch.

Detectable TME signals diminish rapidly with impedance detuning.

Optical experiments cannot conclusively prove the TME effect in thin films.

Abstract

A striking feature of 3 dimensional (3D) topological insulators (TIs) is the theoretically expected topological magneto-electric (TME) effect, which gives rise to additional terms in Maxwell's laws of electromagnetism with an universal quantized coefficient proportional to half-integer multiples of the fine structure constant $\alpha$. In an ideal scenario one therefore expects also quantized contributions in the magneto-optical response of TIs. We review this premise by taking into account the trivial dielectric background of the TI bulk and potential host substrates, and the often present contribution of itinerant bulk carriers. We show that (i) one obtains a non-universal magneto-optical response whenever there is impedance mismatch between different layers and (ii) that the detectable signals due to the TME rapidly approach vanishingly small values as the impedance mismatch is detuned from zero. We demonstrate that it is methodologically impossible to deduce the existence of a TME exclusively from an optical experiment in the thin film limit of 3D TIs at high magnetic fields.