Topological quantum criticality of the disordered Chern insulator

We consider the two-dimensional topological Chern insulator in presence of static disorder. Generic quantum states this system are Anderson localized. However, topology requires a subset critical states, with diverging localization length (the analog ‘center Landau band states’ Hall insulator.) discuss geometric criteria for identification these at weak disorder, and their extension into regime strong disorder by analytical methods. In way, we chart surface embedded phase space spanned energy, control parameter, strength. Our predictions supplemented numerical analysis position multifractal properties.