Detection of Dark Matter Axions via the Quantum Hall Effect in a Resonant Cavity

Abstract

We propose a new method for detecting dark matter axions using a resonant cavity coupled with a quantum Hall system. When a small sample exhibiting quantum Hall effect is placed inside the cavity and the cavity is tuned to resonance, two-dimensional electrons absorb the amplified radiation, leading to a rise in the sample's temperature. By monitoring this temperature increase, the mass $m_a$ of the axion can be inferred. As an example, consider a GaAs sample with surface area $S=0.01\text{cm}^2$ and small thickness $d = 1\,\mu\mathrm{m}$ and its heat capacity $C_s$ at temperature $T = 20\,\mathrm{mK}$. Because the energy flux of the incoming radiation is $P_{ra}\sim 5.9\times10^{-20}\text{W}\,(S/0.01\text{cm}^2)\,(g_{a\gamma\gamma}/10^{-14}\text{GeV}^{-1})^2\,(\sigma/10^7\text{eV})\, (10^{-5}\mbox{eV}/m_a)^3(B/15\text{T})^2 (\rho_d/0.3\rm GeV cm^{-3})$ at the resonance with electrical conductivity $\sigma$ of the cavity wall, the temperature increase is $P_{ra}t_{ob}/C_s \simeq 4.8\mbox{mK}(t_{ob}/1\text{s})(g_{a\gamma\gamma}/10^{-14}\text{GeV}^{-1})^2(20\mbox{mK}/T)^3 (10^{-5}\mbox{eV}/m_a)^3(\sigma/10^7\text{eV})(1\mu \text{m}/d) (B/15\text{T})^2$ with $1\text{T}=10^4$ Gauss where $t_{ob}=1$s is the observation time. It must be smaller than a time constant $\tau>1$s associated with the heat dissipation into thermal bath. Such a large time constant can be realized using superconducting nanowire lead and thin film pedestal supporting the sample dilution refrigerator. The temperature increase $\Delta T\sim 5$mK is detectable using quantum point contact thermometer.