Topological Surface Charge Detection via Terahertz Time-domain Spectroscopy

Abstract

The topological magnetoelectric effect (TME) in three-dimensional topological insulators manifests as a quantized surface charge accumulation proportional to an applied magnetic field. Here we demonstrate an optical method using terahertz time-domain spectroscopy (THz-TDS) to detect surface charge accumulation in a chromium-doped (Bi,Sb)$_2$Te$_3$ thin film under oblique incidence, achieving sub-milliradian Faraday rotation precision. Unlike transport probes that require ultralow longitudinal conductivity, this optical technique is robust against finite $σ_L$, degrading by less than $0.3\%$ even when $σ_L \sim σ_T$. We extract the charge accumulation $η/B_z$ from the measured Faraday rotation and show results at $45^\circ$ and $60^\circ$ coincide within experimental uncertainty. Extending this to axion insulators, we predict that the TME produces an imaginary Faraday rotation linear in frequency, whose slope directly reflects the single-surface charge density. With improved sample thickness and precision, this optical scheme provides a viable pathway toward direct verification of the TME and four-dimensional quantum Hall effect.