  We use the Dirac cone model to explore the high Chern number (C) phases that
are realized in the magnetic-doped topological insulator (TI) multilayer
structures by Zhao et al. [Nature 588, 419 (2020)]. The Chern number is
calculated by capturing the evolution of the phase boundaries with the
parameters and then the Chern number phase diagrams of the TI multilayer
structures are obtained. The high-C behavior is attributed to the band
inversion of the renormalized Dirac cones, along with which the spin
polarization at the \Gamma point will get increased. Moreover, another two TI
multilayer structures as well as the TI superlattice structures are also
studied.
