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The high-Chern number phases with a Chern number C>1 have been observed in arecent experiment that performed on the topological insulator (TI) multilayerstructures, consisting of the alternating magnetic-doped and undoped TI layers.In this paper, we develop an effective method to determine the Chern numbers inthe TI multilayer structures and then make a systematic study on the Chernnumber phase diagrams that are modulated by the magnetic doping and the middlelayer thickness. We point out that in the multilayer structure, the high-Cbehavior can be attributed to the band inversion mechanisms. Moreover, we findthat the lowest bands may be multifold degenerate around the Gamma point, andwhen they are inverted, the Chern number change will be larger than one.Besides the TI multilayer structures implemented in the experiment, we alsoexplore the high-C phase realizations in two other kinds of the TI multilayerstructures. The implications of our results for experiments are discussed.

High-Chern number phase in the topological insulator multilayer structures