  Two-dimensional periodically driven systems can host an unconventional
topological phase unattainable for equilibrium systems, termed the Anomalous
Floquet-Anderson insulator (AFAI). The AFAI features a quasi-energy spectrum
with chiral edge modes and a fully localized bulk, leading to non-adiabatic but
quantized charge pumping. Here, we show how such a Floquet phase can be
realized in a driven, disordered Quantum Anomalous Hall insulator, which is
assumed to have two critical energies where the localization length diverges,
carrying states with opposite Chern numbers. Driving the system at a frequency
close to resonance between these two energies localizes the critical states and
annihilates the Chern bands, giving rise to an AFAI phase. We exemplify this
principle by studying a model for a driven, magnetically doped topological
insulator film, where the annihilation of the Chern bands and the formation of
the AFAI phase is demonstrated using the rotating wave approximation. This is
complemented by a scaling analysis of the localization length for two copies of
a quantum Hall network model with a tunable coupling between them. We find that
by tuning the frequency of the driving close to resonance, the driving strength
required to stabilize the AFAI phase can be made arbitrarily small.
