  We consider a class of fermionic dark matter candidates that are charged
under both the SU(2)$_L$ and U(1)$_Y$ gauge interactions. In this case a
certain amount of dark matter-Higgs couplings, which can split the dark matter
into a pair of Majorana fermions, should be present to evade the constraints
from the dark matter direct detection experiments. These effects may be probed
by means of the dark matter-nucleus scattering via the Higgs-boson exchange
process, as well as the electric dipole moments induced by the dark matter and
its SU(2)$_L$ partner fields. In this article, we evaluate them with an
effective field approach. It turns out that the constraints coming from the
experiments for the quantities have already restricted the dark matter with
hypercharge $Y\geq 3/2$. Future experiments have sensitivities to probe this
class of dark matter candidates, and may disfavor the $Y\geq 1$ cases if no
signal is observed. In this case, only the $Y=0$ and $1/2$ cases may be the
remaining possibilities for the SU(2)$_L$ charged fermionic dark matter
candidates.
