Chern number distribution and quantum phase transition in three-band lattices

Abstract

We numerically study the integer quantum Hall effect on a three-band lattice. With modulating the hopping integral, the peculiar behaviors have been found: (1) Chern numbers of Landau subbands are redistributed; (2) the Hall plateau exhibits a direct transition; (3) there are critical states, where the neighboring two subbands merge together and the pseudogap leads to undefined Chern numbers. By contrast, in the presence of disorder, we find that the higher Hall plateau is sensitive to the disorder and it is always destroyed earlier than lower ones. We also find that the insulator–plateau transition becomes sharper with increasing the size of system. And the critical energy [Formula: see text] gradually shifts to the center of plateau while [Formula: see text] is unaffected with increasing the disorder strength.