  Based on first-principles calculations and effective model analysis, we
propose that the WC-type HfC, in the absence of spin-orbit coupling (SOC), can
host a three-dimensional nodal chain semimetal state. Distinguished from the
previous material IrF4 [T. Bzdusek et al., Nature 538, 75 (2016)], the nodal
chain here is protected by mirror reflection symmetries of a simple space
group, while in IrF4 the nonsymmorphic space group with a glide plane is a
necessity. Moreover, in the presence of SOC, the nodal chain in WC type HfC
evolves into Weyl points. In the Brillouin zone, a total of 30 pairs of Weyl
points in three types are obtained through the first-principles calculations.
Besides, the surface states and the pattern of the surface Fermi arcs
connecting these Weyl points are studied, which may be measured by future
experiments.
