# The lighter side of Dark Matter

Article title: “Absorption of light dark matter in semiconductors”

Authors: Yonit Hochberg, Tongyan Lin, and Kathryn M. Zurek

 Reference: arXiv:1608.01994

Direct detection strategies for dark matter (DM) have grown significantly from the dominant narrative of looking for scattering of these ghostly particles off of large and heavy nuclei. Such experiments involve searches for the Weakly-Interacting Massive Particles (WIMPs) in the many GeV (gigaelectronvolt) mass range. Such candidates for DM are predicted by many beyond Standard Model (SM) theories, one of the most popular involving a very special and unique extension called supersymmetry. Once dubbed the “WIMP Miracle”, these types of particles were found to possess just the right properties to be suitable as dark matter. However, as these experiments become more and more sensitive, the null results put a lot of stress on their feasibility.

Typical detectors like that of LUX, XENON, PandaX and ZEPLIN, detect flashes of light (scintillation) from the result of particle collisions in noble liquids like argon or xenon. Other cryogenic-type detectors, used in experiments like CDMS, cool semiconductor arrays down to very low temperatures to search for ionization and phonon (quantized lattice vibration) production in crystals. Already incredibly successful at deriving direct detection limits for heavy dark matter, new ideas are emerging to look into the lighter side.

Recently, DM below the GeV range have become the new target of a huge range of detection methods, utilizing new techniques and functional materials – semiconductors, superconductors and even superfluid helium. In such a situation, recoils from the much lighter electrons in fact become much more sensitive than those of such large and heavy nuclear targets.

There are several ways that one can consider light dark matter interacting with electrons. One popular consideration is to introduce a new gauge boson that has a very small ‘kinetic’ mixing with the ordinary photon of the Standard Model. If massive, these ‘dark photons’ could also be potentially dark matter candidates themselves and an interesting avenue for new physics. The specifics of their interaction with the electron are then determined by the mass of the dark photon and the strength of its mixing with the SM photon.

Typically the gap between the valence and conduction bands in semiconductors like silicon and germanium is around an electronvolt (eV). When the energy of the dark matter particle exceeds the band gap, electron excitations in the material can usually be detected through a complicated secondary cascade of electron-hole pair generation. Below the band gap however, there is not enough energy to excite the electron to the conduction band, and so detection proceeds through low-energy multi-phonon excitations, with the dominant being the emission of two back-to-back phonons.

In both these regimes, the absorption rate of dark matter in the material is directly related to the properties of the material, namely its optical properties. In particular, the absorption rate for ordinary SM photons is determined by the polarization tensor in the medium, and in turn the complex conductivity, $\hat{\sigma}(\omega)=\sigma_{1}+i \sigma_{2}$ , through what is known as the optical theorem. Ultimately this describes the response of the material to an electromagnetic field, which has been measured in several energy ranges. This ties together the astrophysical properties of how the dark matter moves through space and the fundamental description of DM-electron interactions at the particle level.

In a more technical sense, the rate of DM absorption, in events per unit time per unit target mass, is given by the following equation:

$R=\frac{1}{\rho} \frac{\rho_{D M}}{m_{A^{\prime}}} \kappa_{e f f}^{2} \sigma_{1}$

• $\rho$ – mass density of the target material
• $\rho_{DM}$ – local dark matter mass density (0.3 GeV/cm3) in the galactic halo
• $m_{A'}$ – mass of the dark photon particle
• $\kappa_{eff}$ – kinetic mixing parameter (in-medium)
• $\sigma_1$ – absorption rate of ordinary SM photons

Shown in Figure 1, the projected sensitivity at 90% confidence limit (C.L.) for a 1 kg-year exposure of semiconductor target to dark photon detection can be almost an order of magnitude greater than existing nuclear recoil experiments. Dependence is shown on the kinetic mixing parameter and the mass of the dark photon. Limits are also shown for existing semiconductor experiments, known as DAMIC and CDMSLite with 0.6 and 70 kg-day exposure, respectively.

Furthermore, in the millielectronvolt-kiloelectronvolt range, these could provide much stronger constraints than any of those that currently exist from sources in astrophysics, even at this exposure. These materials also provide a novel way of detecting DM in a single experiment, so long as improvements are made in phonon detection.

These possibilities, amongst a plethora of other detection materials and strategies, can open up a significant area of parameter space for finally closing in on the identity of the ever-elusive dark matter!