- While the Fermi level crosses a region of localized states, the direct conductivity must vanish whereas the Hall conductivity cannot change. (Not obvious)
- Changing the filling factor therefore will force the Fermi level to change continuously within this region of localized states while the Hall conductance will stay constant. This is the main mechanism leading to the existence of plateaux.
Localization is really the KEY to IQHE.
Reference: The Non-Commutative Geometry of the Quantum Hall Effect, https://arxiv.org/pdf/cond-mat/9411052v1.pdf .