Power of Axion Microwave Absorbed by Quantum Hall State in Haloscope

Abstract

We propose a new method for detecting dark matter axions using a resonant cavity coupled to a two-dimensional electron system in the quantum Hall regime. When the cavity is tuned to the axion frequency, the axion-induced electromagnetic field is resonantly enhanced and drives a transverse Hall current in the quantum Hall system. On a quantum Hall plateau, the longitudinal dissipative response is strongly suppressed, $\mathrm{Re}(σ_{xx})\simeq0$, while the Hall conductivity remains finite and quantized, $\mathrm{Re}(σ_{xy})=νe^2/h$. Consequently, the Hall current is essentially nondissipative and introduces only a small additional loss to the cavity, allowing the loaded quality factor to approach the unloaded value, $Q_L\simeq Q_0$. The resulting Hall current is therefore enhanced by the large cavity quality factor, $I_H\propto\mathrm{Re}(σ_{xy})E\propto Q_L$. For a 2D electron density of $3\times10^{11}\mathrm{cm}^{-2}$, filling factor $ν=1/3$, and $Q_L\sim10^5$--$10^6$, we estimate a Hall current of order $I_H\sim10^{-13}$--$10^{-12}\mathrm{A}$ for an axion mass $m_a\sim10^{-5}\mathrm{eV}$ and a magnetic field of order $1.5\times 10^5\mathrm{G}$. The axion mass can be inferred from the resonant frequency, $m_a=2πν_a$. Under the assumed thermal-noise level and readout conditions, the estimated Hall-current signal can achieve a signal-to-noise ratio greater than unity for an observation time of order $100\mathrm{s}$. The proposed method exploits the unique combination of a finite, quantized transverse response and a strongly suppressed longitudinal dissipation in the quantum Hall state, providing an alternative to conventional metallic-antenna detection in axion haloscopes.