Describing the Migdal effect with a bremsstrahlung-like process and many-body effects

Abstract

Recent theoretical studies have suggested that the suddenly recoiled atom struck by dark matter (DM) particle is much more likely to excite or lose its electrons than expected. Such Migdal effect provides a new avenue for exploring the sub-GeV DM particles. There have been various attempts to describe the Migdal effect in liquid and semiconductor targets. In this paper we incorporate the treatment of the bremsstrahlung process and the electronic many-body effects to give a full description of the Migdal effect in bulk semiconductor targets diamond and silicon. Compared with the results obtained with the atom-centered localized Wannier functions (WFs) under the framework of the tight-binding (TB) approximation, the method proposed in this study yields much larger event rates in the low energy regime, due to a ω −4 scaling. We also find that the effect of the bremsstrahlung photon mediating the Coulomb interaction between recoiled ion and the electron-hole pair is equivalent to that of the exchange of a single phonon.

Searches for light dark matter using condensed matter systems

“…[175,176], but it is only in recent years that interest has revived due to the interest in sub-GeV dark matter and the attainment of lower electronic thresholds [133]. The majority of theoretical studies have treated the target material as consisting of individual atomic targets [133,[177][178][179][180][181][182], similar to the original derivation by Migdal, while recently the effect has also been generalized to condensed matter targets [90,160,183]. In principle, if the response function for nuclear recoils is obtained from experimental data, it would contain such contributions, and we could similarly determine the size of the Migdal effect for DM direct detection.…”

“…While the starting point here was a semiclassical approach to the atomic Migdal effect, Refs. [90,160,183] calculated the ionization probability more generally by considering the 2 → 3 process of DM + N → DM + N + e − with second-order perturbation theory in quantum mechanics. One arrives at the same result of Eq.…”

“…Compared to atomic targets of the same element, the rate for the Migdal effect in semiconductors is found to be much larger due to the strong 1/ω 4 e dependence and lower band gap [90,183]. This makes crystal targets with low charge threshold particularly attractive in searching for DMnucleus interactions.…”

“…In Ref. [183], the same authors instead pursued the approach in terms of bremsstrahlung given in Eq. (192), finding much larger rates at low ω e .…”

“…19, calculations of the Migdal effect can be found for Diamond and Si in Ref. [183] and for a limited set of other target materials in Ref. [104].…”