Power of Axion Microwave Absorbed by Quantum Hall State in Haloscope

Abstract

We propose a new method for detecting dark matter axions using haloscope coupled with a quantum Hall system. When a semiconductor sample exhibiting quantum Hall effect is placed inside the haloscope, two-dimensional ( 2D ) electrons absorb the axion induced radiation. We consider a GaAs sample with surface area $S=10{\mathrm{cm}}^2$ and small thickness $\ll 1\mathrm{mm}$. The power is $P_s\simeq 5.2\times 10^{-24}W\left(\frac{g_{\gamma }}{0.36}{)}^2\right(\frac{B_t}{15T}{)}^2\left(\frac{V}{7.2\mathrm{l}}\right)\left(\frac{C}{0.6}\right)\left(\frac{{\rho }_d}{0.45\mathrm{GeVc}{\mathrm{m}}^{-3}}\right),$ where $C$ denotes a form factor of the haloscope with volume $V=\pi R^{2}l\simeq \pi (\frac{2.4}{m_a}{)}^2\times 10^2\mathrm{cm}(\frac{l}{10^2\mathrm{cm}})\simeq 7.2\mathrm{l}$; $g_{\gamma }\simeq 0.36(-0.97)$ for DFSZ ( KSVZ ) axion model. We assume unloaded quality factor $Q_0=10^5$ and quality factor of dark matter axion $Q_a=10^6$. The quality factor $Q_s$ of the sample is that $Q_s\simeq 1.1\times 10^6\left(\frac{10^{-5}\mathrm{eV}}{m_a}\right)\left(\frac{10{\mathrm{cm}}^2}{S}\right)\left(\frac{0.2e^2/h}{\text{Re}({\sigma }_{xx})}\right)$, where we use measured longitudinal electrical conductivity $\text{Re}({\sigma }_{xx})\simeq \frac{0.2e^2}{h}$ ( Planck constant $h$ ) of quantum Hall state. When we put parallelly such $5$ thin samples with identical quantum Hall states, much larger power $P_s\simeq 1.5\times 10^{-23}W$ can be obtained. We have signal to noise ratio $\simeq 2.3\left(\frac{g_{\gamma }}{0.36}{)}^2\right(\frac{B_t}{15T}{)}^2\left(\frac{100\mathrm{mK}}{T}\right)\left(\frac{10^{-5}\mathrm{eV}}{m_a}{)}^{1/2}\right(\frac{V}{7.2\mathrm{l}}\left)\right(\frac{C}{0.6}\left)\right(\frac{{\rho }_d}{0.45\mathrm{GeVc}{\mathrm{m}}^{-3}}\left)\right(\sqrt{\frac{\delta t_{ob}}{100\mathrm{s}}}).$

Comments: 10 pages, 4 figures