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

Abstract

The topological magnetoelectric effect (TME) in three-dimensional topological insulators (TIs), described by $\hat{I}”P=\frac{e^2}{2h}{N}_{\mathrm{Ch}}^{(2)}\hat{I}”B$, 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 $I_{\mathrm{TME}}\propto (C_{\mathrm{total}}/C_{\mathrm{S}})Q_{4D\text{-}\mathrm{QHE}}$, where the signal is suppressed by the capacitance ratio $C_{\mathrm{total}}/C_{\mathrm{S}}$. Here we propose an active compensation scheme that introduces a tunable negative capacitance $C_{\mathrm{comp}}\approx -C_{\mathrm{gate}}$ into the gate line, effectively canceling the gate dielectric capacitance and driving $C_{\mathrm{total}}/C_{\mathrm{S}}\to 1$. We validate the method using a quantum anomalous Hall (QAH) device, which shares the same surface-state physics with 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 promising pathway toward direct measurements of the 4D QHE.