Axion Dark Matter and Plateau-Plateau Transition in Quantum Hall Effect

Axion dark matter inevitably generates electromagnetic radiation in quantum Hall effect experiments that use strong magnetic fields. Although these emissions are very weak, we have shown using a QCD axion model that they influence the plateau-plateau transition at low temperatures (below $100$ mK) in a system with a large surface area (greater than $10^{-3}\rm cm^2$) of two-dimensional electrons. By analyzing previous experiments that show saturation of the transition width $\Delta B$ as temperature and microwave frequency change, we provide evidence for the presence of axions. Notably, in most experiments without axion effects, the saturation frequency $f_s(T)$ is less than $1$ GHz at temperatures of $100$ mK or higher and for system sizes of $10^{-3}\rm cm^2$ or smaller. Additionally, the frequency $f_s(T)$ decreases with decreasing temperature or increasing system size. However, there are experiments that show a saturation frequency $f_s(T)\simeq 2.4$GHz despite a low temperature of 35 mK and a large surface area of $6.6\times 10^{-3}\rm cm^2$ for the Hall bar. This identical frequency of approximately $2.4$ GHz has also been observed in different plateau transitions and in Hall bars of varying sizes. These unexpected results are caused by axion microwaves. The saturation frequency $f_s=m_a/2\pi$ of $\simeq 2.4$ GHz implies an axion mass of $\simeq 10^{-5}$eV. By comparing the axion effect with thermal effect on the width $\Delta B$, we have shown the dominance of the axion effect over thermal effect at low temperature less than $50$mK. The dominance of the axion effect is attributed to significant absorption of axion energy, which is proportional to the square of the number of electrons involved.