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

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 $T=20\mathrm{m}\mathrm{K}$. Because the energy flux of the incoming radiation is $P_{ra}\sim 5.9\times {10}^{-20}\text{W}(S\mathrm{/}0.01{\text{cm}}^2)(g_{a\gamma \gamma }\mathrm{/}{10}^{-14}{\text{GeV}}^{-1}{)}^2(\sigma \mathrm{/}{10}^7\text{eV})({10}^{-5}eV\mathrm{/}{m}_a{)}^3(B\mathrm{/}15\text{T}{)}^2({\rho }_d\mathrm{/}0.3\mathrm{G}\mathrm{e}\mathrm{V}\mathrm{c}{\mathrm{m}}^{-3})$ at the resonance with electrical conductivity $\sigma$ of the cavity wall, the temperature increase is $P_{ra}{t}_{ob}\mathrm{/}{C}_s\simeq 4.8mK(t_{ob}\mathrm{/}1\text{s})(g_{a\gamma \gamma }\mathrm{/}{10}^{-14}{\text{GeV}}^{-1}{)}^2(20mK\mathrm{/}T{)}^3({10}^{-5}eV\mathrm{/}{m}_a{)}^3(\sigma \mathrm{/}{10}^7\text{eV})(1\mu \text{m}\mathrm{/}d)(B\mathrm{/}15\text{T}{)}^2$ 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 $\mathrm{\Delta }T\sim 5$mK is detectable using quantum point contact thermometer.