which can be taken as smoking-gun signals of DM scattering, can further increase an exper-iment’s constraining power. For DM–nucleon interactions, although the elastic scattering is the best channel, however, for light DM particles which can not deposit observable energies in detectors, one has to rely on the high energy part of ionization processes.

The energy and momentum transfers involved in sub-GeV DM scattering overlap typ-ical atomic scales, so studies of issues such as binding effects and electron/nuclear recoil mechanism, which play important roles in interpreting experimental data, require detailed many-body calculations. This case study of hydrogen, where both binding and recoil can be taken into account most simply, therefore provides useful qualitative understanding of what to be anticipated in sub-GeV DM scattering off practical detector materials such as germanium and xenon.

# ACKNOWLEDGMENTS

We acknowledge the support from the Ministry of Science and Technology of Republic of China under Grants No. 102-2112-M-002-013-MY3 (J.-W. C., C.-L. W., and C.-P. W.) and No. 103-2112-M-259-003 (H.-C. C. and C.-P. L.); the Center for Theoretical Sciences and Center of Advanced Study in Theoretical Sciences of National Taiwan University (J.-W. C., C.-L. W., and C.-P. W.); and the National Center for Theoretical Sciences. J.-W. C. was also supported in part by the Deutsche Forschungsgemeinschaft and National Natural Science Foundation of China (CRC 110).

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