Search for Light Dark Matter from the Atmosphere in PandaX-4T.

We report a search for light dark matter produced through the cascading decay of η mesons, which are created as a result of inelastic collisions between cosmic rays and Earth's atmosphere. We introduce a new and general framework, publicly accessible, designed to address boosted dark matter specifically, with which a full and dedicated simulation including both elastic and quasielastic processes of Earth attenuation effect on the dark matter particles arriving at the detector is performed. In the PandaX-4T commissioning data of 0.63  tonne·year exposure, no significant excess over background is observed. The first constraints on the interaction between light dark matter generated in the atmosphere and nucleus through a light scalar mediator are obtained. The lowest excluded cross section is set at 5.9×10^{-37}  cm^{2} for a dark matter mass of 0.1  MeV/c^{2} and mediator mass of 300  MeV/c^{2}. The lowest upper limit of η to the dark matter decay branching ratio is 1.6×10^{-7}.