  A Dirac fermion in a topological Dirac semimetal is a quadruple-degenerate
quasi-particle state with a relativistic linear dispersion. Breaking either
time-reversal or inversion symmetry turns this system into a Weyl semimetal
that hosts double-degenerate Weyl fermion states with opposite chiralities.
These two kinds of quasi-particles, although described by a relativistic Dirac
equation, do not necessarily obey Lorentz invariance, allowing the existence of
so-called type-II fermions. Recent theoretical discovery of type-II Weyl
fermions evokes the prediction of type-II Dirac fermions in PtSe$_2$-type
transition metal dichalcogenides, expecting an experimental confirmation. Here,
we report an experimental realization of type-II Dirac fermions in PdTe$_2$ by
angle-resolved photoemission spectroscopy combined with {\it ab-initio} band
calculations. Our experimental finding makes the first example that has both
superconductivity and type-II Dirac fermions, which turns the topological
material research into a new phase.
