  Recently XENON1T Collaboration announced that they observed some excess in
the electron recoil energy around a 2-3 keV. We show that this excess can be
interpreted as exothermic scattering of excited dark matter (XDM), $XDM +
e_{atomic} \rightarrow DM + e_{free}$ on atomic electron through dark photon
exchange. We consider DM models with local dark $U(1)$ gauge symmetry that is
spontaneously broken into its $Z_2$ subgroup by Krauss-Wilczek mechanism. In
order to explain the XENON1T excess with the correct DM thermal relic density
within freeze-out scenario, all the particles in the dark sector should be
light enough, namely $\sim O(100)$ MeV for scalar DM and $\sim O(1-10)$ MeV for
fermion DM cases. And even lighter dark Higgs $\phi$ plays an important role in
the DM relic density calculation: $X X^\dagger \rightarrow Z' \phi$ for scalar
DM ($X$) and $\chi \bar{\chi} \rightarrow \phi \phi$for fermion DM ($\chi$)
assuming $m_{Z'} > m_\chi$. Both of them are in the $p$-wave annihilation, and
one can easily evade stringent bounds from Planck data on CMB on the $s$-wave
annihilations, assuming other dangerous $s$-wave annihilations are
kinematically forbidden.
