Dark Matter Detection Using Phonon Sensing in Amorphous Materials

Abstract

We present a concept for a tabletop-scale detector with an amorphous target designed to search for dark matter absorption into phonon excitations. In crystalline materials, absorption occurs only at narrow resonances where the dark matter mass matches a zero momentum optical phonon mode, whereas amorphous targets provide a broadband response that can substantially enhance the absorption rate away from these resonances. The predicted backgrounds arise from the relaxation of disorder-induced metastable defects in the amorphous target, as well as from low-energy noise intrinsic to superconducting phonon sensors. A prototype detector with a target mass of only a few $μ$g could provide broadband sensitivity to dark photon absorption across the 50 meV-200 meV mass range, probing up to two orders of magnitude beyond existing constraints.

Figures (10)

• Figure 1: The maximal expected number of absorption events from dark photon dark matter for both amorphous (solid) and crystalline (dashed) targets, where at each $m_{A'}$ we take the dark photon mixing parameter $\kappa$ to saturate the upper limits derived from the XENON experiment An:2020bxdXENON:2021qze. For c-SiO$_2$, we indicate the regions more than 5 linewidths from the resonances by dotted lines, as the estimate of the excitation rate for these energies is merely an interpolation. See \ref{['app:ELFs']} for more details and references.
• Figure 2: Conceptual design of the amorphous detector. The detector consists of thin amorphous dielectric membranes (green) suspended on the top of a silicon frame (blue). The membrane is etched into strips and the signals are read out by the two superconducting sensors on the two ends of the strips, TESs are drawn as an example. The white areas are openings in the membrane, separating the strips from one another, to improve phonon collection efficiency. The fiducial target volume consists of the middle region of the strips (highlighted by the blue box), as detailed in \ref{['app:detector']}.
• Figure 3: Exclusion sensitivity of the conceptual detector, along with existing bounds (gray shading) An:2020bxdXENON:2021qze. The solid lines are median sensitivity assuming the TLS background rate as calculated in \ref{['app:background']}. The dark and light shadow bands indicate $10\%,~30\%,~70\%$, and $90\%$ percentiles of the sensitivity projection. The dashed (dotted) lines are ideal sensitivity assuming no backgrounds with 1µg yr (1mg yr) exposure; they are not expected to be attainable and included only to illustrate the effect of the background on the expected sensitivity. The detector resolution is assumed to be dominated by the quasiparticle Fano noise, as quantified in \ref{['app:detector']}.
• Figure 4: Top: Mean free path as a function of vibration energy for amorphous $\text{SiO}_2$PhysRevB.4.2029. The vertical dashed line indicates the energy threshold for a phonon to break a Cooper pair in the Al phonon collectors. The thicker vertical dashed line corresponds to transition between Rayleigh- and TLS-dominated scattering. Bottom: Characteristic timescales in a thin film of amorphous $\text{SiO}_2$. The Thouless time is computed for the distance from the center of the strip to the phonon collectors ($L\approx 250\,\mu$m).
• Figure 5: Phonon collection efficiency as a function of target strip length. The Al phonon collector is $25\,\mu\text{m}\times 100\,\mu\text{m}$ on each end of the strip. The high aspect ratio of the $25\,\mu\text{m}$ collection width to the $2\,\mu\text{m}$ target film thickness ensure that no phonons escape to the outside of the strip. The phonon velocity is $3.7\,\text{mm}/\mu\text{s}$, mean free path is $10\,\mu m$, and the phonon lifetime is $0.66\,\text{ms}$, assuming all phonons are at energy $2\Delta_\mathrm{Al}$.