Redistributing Chern numbers and quantum Hall transitions in multi-band lattices

We numerically study the integer quantum Hall effect (IQHE) on m-band lattices. With continuous modulating the next-nearest-neighbor hopping integral t', it is found that the full band is divided into 2m−1 regions. There are m−1 critical regions with pseudogaps induced by the merging between the two adjacent subbands, where both Chern numbers of the correlating Landau subbands and the corresponding Hall plateau are not well-defined. The other m regions with different well-defined Chern numbers are separated by the above m−1 critical regions. Due to the redistributing Chern numbers of system induced by the merging of subbands, the Hall conductance exhibits a peculiar phase transition, which is characterized by the direct change of Hall plateau state.