Detectable electric current induced by the dark matter axion in a conductor

We propose a method of detecting the dark matter axion by using two slabs of a conductor. The flat surfaces are set face to face, parallel to each other. An external magnetic field B parallel to the surfaces is applied. Radiation converted from the axion arises between the two slabs. When we tune the spacing l between the two surfaces such that l = π/ma with axion mass ma, a resonance occurs so that the radiation becomes strong. Furthermore, the electric current flowing on the surface of the slabs is enhanced. We show that the electric current is large enough to be detectable at the resonance. It reaches 0.7 × 10−9 A $(10^{-5}\, \mbox{eV}/m_a)^{1/2} \, (B/5\, \mbox{T}) \, (L/10\, \mbox{cm}) \, (\sigma /3.3\times 10^7 \, \rm eV)$ using 6N copper for the square slabs with side length L and high electrical conductivity σ at temperature T ∼ 1 K. The power of the Joule heating is $0.3\times 10^{-22} \, \mbox{W} \, (B/5 \, \mbox{T})^2 \, (10^{-5} \, \mbox{eV}/m_a)^{1/2} \, (L/10 \, \mbox{cm})^2 \, (\sigma /3.3\times 10^7 \, \rm eV)$. When we amplify the power using an LC circuit with factor QLC, the signal-to-noise ratio is $4.5\times 10^{4} \, (Q_\mathrm{LC}/10^6) \, (B/5 \, \mbox{T})^2 \, (t_\mathrm{obs}/1\, \mathrm{s})^{1/2}\, (10^{-5} \, \mbox{eV}/m_a) \, (L/10 \, \mbox{cm})^2 \, (\sigma /3.3\times 10^7 \, \rm eV)$ with an observation time of tobs.