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Quantum anomalous Hall (QAH) multilayers provide a platform of topologicalmaterials with high Chern numbers. We investigate the localization routes ofbilayer QAH systems with Chern number C = 2 under strong disorder, by numericalsimulations on their quantum transport properties and the Chern-Simons axioncoupling. Compared to the single layer counterpart with C = 2, the localizationtrajectories present much richer behaviors, for example, the existence of thestable intermediate state with C = 1 can be tuned by model parameters. Thisstate was always unstable in the single layer case. Furthermore, the twoparameter scaling trajectories also exhibit multiple patterns, some of whichwere not captured by the standard Pruisken picture. During the process towardslocalization, the Chern-Simons axion coupling shows a surprisingly remarkablepeak which is even higher and sharper in the large size limit. Therefore thedisordered bilayer QAH system can be a good candidate for this nontrivialmagnetoelectric coupling mediated by orbital motions.

Localization Trajectory and Chern-Simons axion coupling for Bilayer Quantum Anomalous Hall Systems