Vacancy-driven topological transition of a Chern insulator

Abstract

We develop a microscopic description of the strong-disorder transition in a Chern insulator using the in-gap ring states bound to individual vacancies. Using Green's function formalism, we construct an energy-dependent Hamiltonian describing their hybridization. In a commensurate periodic vacancy lattice, a Dirac inversion of the zero-energy vacancy kernel accounts for the change in the occupied-state Chern number of the full system. We treat weak positional disorder using the self-consistent Born approximation and numerical disorder averaging, and study independently distributed vacancies using transfer-matrix and multifractal scaling. The local Chern marker and current textures track the transition in real space. Together, these results highlight the role that nonperturbative ring states have as microscopic degrees of freedom through which strong disorder destroys the Chern phase.