  Due to the low nuclear recoils, sub-GeV dark matter (DM) is usually beyond
the sensitivity of the conventional DM direct detection experiments. The
boosted and Migdal scattering mechanisms have been proposed as two new
complementary avenues to search for light DM. In this work, we consider the
momentum-transfer effect in the DM-nucleus scattering to derive the new bounds
on sub-GeV DM for these two scenarios. We show that such an effect is sizable
so that the existing bounds on the DM-nucleus scattering cross section can be
improved significantly.
