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

TL;DR

This work introduces a novel axion dark matter detector that combines a resonant cavity with a quantum Hall sample. Axion-induced microwaves, amplified at cavity resonance, are fully absorbed by the 2D electron gas in the quantum Hall state, producing a measurable temperature rise that encodes the axion mass $m_a$ and coupling $g_{a\gamma\gamma}$. The authors provide quantitative estimates for a GaAs-based, ultra-low-temperature setup, deriving the absorbed power $P_{ra}$, the resulting temperature change $\Delta T$, and the dependence on system parameters such as $B$, $d$, $\tau$, and $\rho_d$, along with a practical cavity-scanning strategy to cover a range of $m_a$. This approach yields a new detection channel for high-mass axions (beyond traditional cavity searches) and offers a pathway to determine $m_a$ and $g_{a\gamma\gamma}$ via thermally induced signals in a quantum Hall medium.

Abstract

We propose a new method for detecting dark matter axions using a resonant cavity coupled with a quantum Hall system. When a 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 small thickness $d = 0.1\,μ\mathrm{m}$ and its heat capacity $C_s$ at temperature $T = 20\,\mathrm{mK}$. According to the QCD axion model, because the energy flux of the incoming radiation is $P_{ra}\sim 10^{-18}g_γ^2\mbox{W cm}^{-2}(10^{-5}\mbox{eV}/m_a)(B/1.5\times 10^5\mbox{Gauss})^2 (ρ_d/0.3\rm GeV cm^{-3})$ at the resonance with $g_γ(\rm KSVZ)=-0.96$ and $g_γ(\rm DFSZ)=0.37$, the temperature increase $(P_{ra}/C_s)\times τ$ is approximately $\simeq 0.25(\mbox{mK})(τ/10\mbox{ms})\,g_γ^2\,(20\mbox{mK}/T)^3(10^{-5}\mbox{eV}/m_a)(B/1.5\times 10^5\mbox{Gauss})^2(0.1μ\mbox{m}/d)$, where $τ$ is the time constant associated with the heat dissipation into thermal bath.

Figures (3)

• Figure 1: Density of state $\rho(E)$ in finite sample. There is a region in which states are extended over the sample, while states in other region are localized. Dotted line represents Fermi energy $E_f$
• Figure 2: Slabs parallel to each other separated with distance $l$. Sample tilted with $\theta=\pi/6$ to $y$ axis and parallel to $x$ axis.
• Figure 3: When we do not observe $\Delta T$ larger than $0.5\text{mK}(\tau/10\text{ms})$ with time constant $\tau=10$ms, the value of $g_{a\gamma\gamma}$ above the dashed line denoted with $0.5\text{mK}(\tau/10\text{ms})$ is excluded. We roughly show excluded region obtained by CAPP.