  The search for singlet fermion dark matter at high-energy colliders is
commonly analyzed with a singlet scalar mediator, which however violates the
standard model (SM) gauge invariance, renormalizability and unitarity. These
problems can be cured by introducing a mixing between the singlet scalar $s$
and the SM Higgs boson $h$. Thus one has to consider two scalar mediators $h_1$
and $h_2$, where $h_1$ is identified as the discovered 125 GeV Higgs boson. As
a specific example, we consider the dark matter (DM) search in the $t \bar{t} +
E_{T}^{\text{miss}}$ channel. According to the masses of dark matter and two
scalar mediators, we classify the process into four cases. By investigating the
total cross sections and differential distributions, we find that the
contribution of the 125~GeV Higgs boson $h_1$ cannot be neglected in all cases
and can even dominate once $h_1$ is on-shell in dark matter production.
Further, we study the impact of $h_1$ on the LHC bounds of dark matter searches
in the hadronic and semileptonic channels with the integrated luminosity of
$36~\text{fb}^{-1}$. Finally we make a brief comment that $h_1$ should be also
considered in the vector DM search at high-energy colliders.
