Axion Detection with Quantum Hall Effect

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.