Topological Surface Charge Detection via Active Capacitive Compensation: A Pathway to the 4D Quantum Hall Effect

The topological magnetoelectric effect (TME) in three-dimensional topological insulators (TIs), described by ΔP=(e^{2}/2h)N_{Ch}^{(2)}ΔB, serves as a condensed-matter realization of the four-dimensional quantum Hall effect (4D QHE). In dual-gate axion insulator devices, the TME-induced polarization yields a current I_{TME}∝(C_{total}/C_{S})Q_{4D-QHE}, where the signal is suppressed by the capacitance ratio C_{total}/C_{S}. Here we propose an active compensation scheme that introduces a tunable negative capacitance C_{comp}≈-C_{gate} into the gate line, effectively canceling the gate dielectric capacitance and driving C_{total}/C_{S}→1. We validate the method using a quantum anomalous Hall (QAH) device, which shares the same surface-state physics as the axion insulator but permits direct charge measurement via a single gate, recovering over 95% of the quantized charge signal from an initially half-attenuated state. This compensation method provides a robust means of resolving minute TME signals, offering a pathway toward direct measurements of the 4D QHE.