Phonon dynamics for light dark matter detection

The search for low-mass dark matter (DM) goes in parallel with the identification of new detection channels and the development of suitable detectors. Detection of the resulting small energy depositions is challenging: it requires extremely high sensitivity, only achievable by cryogenic thermal detectors, which might be put to the limit. Understanding the processes which can limit performances of these detectors can be thus crucial for evaluating the feasibility of the proposed new detection schemes and to design the detectors and tune their performance. In this paper we focus on a promising detection scheme, the excitation of single optical phonons in polar materials, to evaluate one of the possible limiting factors of cryogenic thermal detectors, i.e. the phonon dynamics in the target/absorber. We present a detailed theoretical analysis, within an entirely ab initio scheme, of the downconversion and propagation processes undergone by optical phonons, created by the interaction of a low-mass DM particle in an Al2O3 target, until they reach the interface with a phonon Al collector. After a preliminary methodological survey that reveals the limitations of any Relaxation Time Approximation based method, we developed a 3D beyond-RTA phonon Monte Carlo that allowed us to introduce the spatial dimension of the device and address questions about impact of target size and scattering position. We analyse also the effect of the phonon energy and wavevector and show that isotopes can, perhaps counterintuitively, result in a larger heat flux by providing transport channels of higher velocities, thus favoring detection. Our results suggest that, though challenging, the direct detection of light DM via athermal phonon generation appears feasible, and that the phonon downconversion followed by quasi-ballistic propagation does not appear to be a major bottleneck in terms of reducing the signal.