  Plateau-plateau transition in integer quantum Hall effect is a phase
transition between metal and insulator. The behavior how the width $\Delta B$
of the transition changes with temperature and frequency of radiations imposed
has been explored extensively. It decreases with the decrease of temperature
and frequency, but saturates at critical temperature or frequency. We have
recently discussed the effect of axion dark matter on the saturation. The axion
generates radiations under strong magnetic field in the experiment of quantum
Hall effect. The radiations play a similar role to the one of radiations
imposed externally. In this paper we discuss in detail how the width behaves in
temperature and frequency under the effect of axion dark matter. We show that
the axion effect can be observable in low temperature roughly below $100$mK.
According to our detailed analysis of the saturation, we find that critical
frequency of saturation observed in previous experiment strongly suggests axion
mass $m_a=(0.95\sim 0.99)\times 10^{-5}$eV.
