$\nu$ limits from Super-Kamiokande on dark matter-electron scattering in the Sun

Particle dark matter scattering on electrons in the Sun may gravitationally capture and self-annihilate inside it to neutrinos and anti-neutrinos, or other final states that in turn decay to them. Using up-to-date measurements by Super-Kamiokande of the fluxes of atmospheric electron-type and muon-type neutrinos, we set the most stringent limits on the electron scattering cross sections of dark matter down to about $10^{-40}-10^{-39}$ cm$^2$ over a mass range of 4$-$200 GeV. These outdo direct searches for dark matter-electron scattering and previously set limits at IceCube. We also derive corresponding reaches at Hyper-K, and show that atmospheric neutrino observations restricted to the direction of the Sun can improve sensitivities.