  Recently, a new "type-II" Weyl fermion, which exhibits exotic phenomena such
as angle-dependent chiral anomaly, was discovered in a new phase of matter
where electron and hole pockets contact at isolated Weyl points. [Nature
\textbf{527}, 495 (2015)] This raises an interesting question whether its
counterpart, i.e., type-II \textit{Dirac} fermion, exists in real materials.
Here, we predict the existence of symmetry-protected type-II Dirac fermions in
a class of transition metal dichalcogenide materials. Our first-principles
calculations on PtSe$_2$ reveal its bulk type-II Dirac fermions which are
characterized by strongly tilted Dirac cones, novel surface states, and exotic
doping-driven Lifshitz transition. Our results show that the existence of
type-II Dirac fermions in PtSe$_2$-type materials is closely related to its
structural $P\bar{3}m1$ symmetry, which provides useful guidance for the
experimental realization of type-II Dirac fermions and intriguing physical
properties distinct from those of the standard Dirac fermions known before.
