Quantum Anomalous Hall Effect with Higher Plateaus*

The quantum anomalous Hall (QAH) effect in magnetic topological insulators is driven by the combination of spontaneous magnetic moments and spin-orbit coupling. Its recent experimental discovery raises the question if higher plateaus can also be realized. Here, we present a general theory for a QAH effect with higher Chern numbers and show by first-principles calculations that a thin film magnetic topological insulator of Cr-doped Bi2(Se,Te)3 is a candidate for the C$=$ 2 QAH insulator. Remarkably, whereas a higher magnetic field leads to lower Hall conductance plateaus in the integer quantum Hall effect, a higher magnetic moment leads to higher Hall conductance plateaus in the QAH effect.