A Way of Determination of Axion Mass with Quantum Hall Effect

Abstract

Axion dark matter is converted to electromagnetic radiations in the presence of strong magnetic field. The radiations possibly give rise to non trivial phenomena in condensed matter physics. Especially, we discuss that saturation of plateau-plateau transition width observed at low temperature in integer quantum Hall effect is caused by the axion. The radiations from axions are inevitably present in the experiment. Although the radiations generated by axion is extremely weak, Hall conductivity jumps up to next plateau even if only a single electron occupies an extended state; a localized electron is transited to the extended state by absorbing the radiation. According to our analysis, previous experiment\cite{sat6} of the saturation in detail suggests that the axion mass is in the range $10^{-5}\mbox{eV}\sim 10^{-6}$eV. We propose a way of the determination of the axion mass by imposing microwaves on Hall bar and also a way of the confirmation that the axion really causes the saturation of the width.