Diurnal modulation of electron recoils from DM-nucleon scattering through the Migdal effect

Halo dark matter (DM) particles could lose energy due to the scattering off nuclei within the Earth before reaching the underground detectors of DM direct detection experiments. This Earth shielding effect can result in diurnal modulation of the DM-induced recoil event rates observed underground due to the self-rotation of the Earth. For electron recoil signals from DM-electron scatterings, the current experimental constraints are very stringent such that the diurnal modulation cannot be observed for halo DM. We propose a novel type of diurnal modulation effect: diurnal modulation in electron recoil signals induced by DM -nucleon scattering via the Migdal effect. We set so far the most stringent constraints on DM-nucleon scattering cross section via the Migdal effect for sub-GeV DM using the S2 -only data of PandaX-II and PandaX-4T with improved simulations of the Earth shielding effect. Based on the updated constraints, we show that the Migdal effect induced diurnal modulation of electron events can still be significant in the low energy region, and can be probed by experiments such as PandaX-4T in the near future.