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