Capacitance Measurements of a Quantum Anomalous Hall Insulator*

Topological effects in zero magnetic field are currently of high interest. The quantum anomalous Hall effect, one such topological effect, features a Hall resistance quantized to ±h/e² at zero magnetic field, which can be realized in magnetically doped topological insulators. The net transport current in the quantum anomalous Hall effect is thought to be carried by dissipationless edge states, with the bulk dominated by localized non-conducting states. Recent works investigating the electrostatic potential and local current density in the quantum anomalous Hall effect have suggested that transport current flows primarily in the bulk at some carrier densities. Going beyond the traditional transport measurements, here we report capacitance measurements of a Cr-doped (Bi,Sb)₂Te₃ quantum anomalous Hall insulator to probe the conductive behavior of the entire sample surface.