Erratum: Phonon-mediated Migdal effect in semiconductor detectors (Physical Review D (2022) 106 (043004) DOI: 10.1103/PhysRevD.106.043004)

In this paper, we proposed to describe the Migdal effect in semiconductor in the picture where an electron-hole pair is excited via phonon mediators, accompanied by a multiphonon process triggered by an incident dark matter (DM) particle, so that the generation of phonons, and the excitation of the electron-hole pairs, as well as the medium effect in solids can be fabricated into a common framework. Using the formula we derived in Eq. (3.4), one can effectively push the sensitivities of the semiconductor targets down to the MeV DM mass region. In this Erratum, we correct an error in our original numerical implementation of Eq. (3.4). To be specific, we omitted the contribution of T0(E)=d(E) in the integration in Eq. (3.4), which corresponds to the process where an electron-hole pair is excited without generating any phonons, and consequently the Migdal event rate in the small- q regime was remarkably underestimated. While the effectiveness of the formula Eq. (3.4) is not affected, after T0(E) is included, it is found that Migdal event rates calculated using the phonon-mediated approach and using the bremsstrahlung-like expression Eq. (3.6) coincide quite well even in the low dark matter mass region (see Fig. 1), which indicates a broader scope of application of the impulse approximation. (Figure Presented).