Dark antiatoms can explain DAMA
  We show that the existence of a sub-dominant form of dark matter, made of dark antiatoms of mass and size of the order of 1 TeV and 30 fm respectively, can explain the results of direct detection experiments, with a positive signal in DAMA/NaI and DAMA/LIBRA and no signal in other experiments. The signal comes from the binding of the dark antiatoms to thallium, a dopant in DAMA, and is not present for the constituent atoms of other experiments. The dark antiatoms are made of two particles oppositely charged under a dark U(1) symmetry and can bind to terrestrial atoms because of a kinetic mixing between the photon and the massless dark photon, such that the dark particles acquire an electric millicharge of the order of 0.0005e. This millicharge enables them to bind to high-Z atoms via radiative capture, after they thermalize in terrestrial matter through elastic collisions. 
Quentin Wallemacq, Jean-Ren\'e Cudell
hep-ph