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\Big(\frac{g_{\gamma}}{0.36}\Big)^2 \Big(\frac{B_t}{15T}\Big)^2\Big(\frac{V}{7.2\, \mathrm{l}}\Big)\Big(\frac{C}{0.6}\Big) \Big(\frac{\rho_d}{0.45\mathrm{GeVcm^{-3}}}\Big), $ where $C$ denotes a form factor of the haloscope with volume $V= \pi R^2l \simeq \pi\Big(\frac{2.4}{m_a}\Big)^2\times 10^2\mathrm{cm}\Big(\frac{l}{10^2\mathrm{cm}}\Big)\simeq 7.2\,\mathrm{l}$; $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 $Q_s\simeq 1.1\times 10^6\Big(\frac{10^{-5}\mathrm{eV}}{m_a}\Big)\Big(\frac{10\mathrm{cm}^2}{S}\Big) \Big(\frac{0.2e^2/h}{\text{Re}(\sigma_{xx})}\Big)$, 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\,\Big(\frac{g_{\gamma}}{0.36}\Big)^2 \Big(\frac{B_t}{15T}\Big)^2\Big(\frac{100\mathrm{mK}}{T}\Big) \Big(\frac{10^{-5}\mathrm{eV}}{m_a}\Big)^{1/2}\Big(\frac{V}{7.2\, \mathrm{l}}\Big) \Big(\frac{C}{0.6}\Big)\Big(\frac{\rho_d}{0.45\mathrm{GeVcm^{-3}}}\Big) \Big(\sqrt{\frac{\delta t_{ob}}{100\mathrm{s}}}\Big). $