Topological Surface Charge Detection via Terahertz Time-domain Spectroscopy
The topological magnetoelectric effect (TME) is a condensed-matter realization of the four-dimensional quantum Hall effect (4D-QHE), manifesting as quantized surface charge accumulation proportional to an applied magnetic field. To date, however, no optical technique has been developed to directly probe this charge accumulation. Here, we demonstrate a terahertz time-domain spectroscopy method for direct detection of surface charge accumulation---a physical quantity relevant to both the 4D-QHE and 2D-QHE, in sharp contrast to the previous optical measurements, which focused on the Hall conductivity $σ_{xy}$ of the 2D-QHE. Using a chromium-doped (Bi,Sb)$_2$Te$_3$ thin film, we achieve sub-milliradian Faraday rotation precision. Extending this scheme to axion insulators, we predict that the TME gives rise to an imaginary Faraday rotation linear in frequency, whose slope directly reflects the single-surface charge density. With further improvements in sample thickness and precision, this approach offers a viable pathway toward direct verification of the TME and 4D-QHE.