Trajectory of the anomalous Hall effect towards the quantized state in a ferromagnetic topological insulator

Topological insulators are bulk electronic insulators with symmetry-protected gapless modes on their surfaces(1-5). Breaking time-reversal symmetry in these systems via ferromagnetism induces a gapped state characterized by a zero magnetic field quantized Hall response-the quantum anomalous Hall (QAH) state(6-8). A key question that has remained experimentally unexplored is the relationship of this new type of quantum Hall (QH) state with the previously known orbitally driven QH states. Here, we show experimentally that a ferromagnetic topological insulator exhibiting the QAH state is well described by the global phase diagram of the QH effect. By mapping the conductivity tensor in the vicinity of the QAH phase, we find evidence for quantum criticality and delocalization behaviour(9,10) that can quantitatively be described by the renormalization group properties of the QH ground state(11,12). This result demonstrates that this QAH state can be understood within the context of the law of corresponding states that governs the QH state(13,14).