Extended Data Figure 7: Identification of the QAH region in the capacitance device (device 6).
From: Quantum anomalous Hall effect from intertwined moiré bands
a–d, Normalized differential top-gate capacitance, \(C/{C}_{g}\), versus magnetic field and filling factor at 300 mK. Results for four different electric fields are shown. Most strongly dispersive incompressible states shown arise from the Landau levels of the graphite top gate and are irrelevant in this study. The black dashed lines, originated from \(\nu =1\), are the theoretical magnetic-field dispersion of a QAH state with Chern number -1. We use this to determine the Mott-QAH insulator boundary in Fig. 3c of the main text. The system is a Mott insulator in a since there is no magnetic field dispersion of the incompressible state; it is near the Mott-QAH insulator boundary in b; and it is a QAH insulator in c, d. The QAH insulator-metal boundary is determined as capacitance reaches \(C/{C}_{g}\approx 1\) in the metallic state. e, Electric-field dependence of \(C/{C}_{g}\) at \(\nu =1\), 300 mK and zero magnetic field. The QAH region determined from a–d is shaded in blue. The normalized capacitance \(C/{C}_{g}\) equals to 1 for a metallic state at large electric fields. It is below 1 for incompressible states, which include both the Mott and QAH insulating states. Charge gap closure (i.e. \(C/{C}_{g}\) = 1) is not observed at the Mott-QAH phase boundary.
