  We propose a new kind of Dark Matter: Derivative Portal Dark Matter. This
kind of Dark Matter connects to the Standard Model through a massive mediator,
which links to the Standard Model in derivative form. The derivative of a
mediator in momentum space corresponds to the mediated momentum, which vanishes
in the zero momentum transfer limit. As a result, this kind of Dark Matter can
evade stringent constraint from the Dark Matter direct detection while fitting
the Dark Matter relic density observation naturally.
