  The distinct over-tilting of band crossings in topological semimetal
generates the type-I and typeII classification of Dirac/Weyl and nodal-line
fermions, accompanied by the exotic electronic and magnetic transport
properties. In this work, we propose a concept of hybrid nodal-chain semimetal,
which is identified by the linked type-I and type-II nodal rings in the
Brillouin zone. Based on first-principles calculations and swarm-intelligence
structure search technique, a new ternary nitride MgCaN2 crystal is proposed as
the first candidate to realize a novel 3D hybrid nodal-chain state. Remarkably,
a flat band is emergent as a characteristic signature of such a hybrid
nodal-chain along certain direction in the momentum space, thereby serving a
platform to explore the interplay between topological semimetal state and flat
band. Moreover, the underlying protection mechanism of the hybrid nodal-chain
is revealed by calculating the mirror Z2 invariant and developing a k.p
effective Hamiltonian. Additionally, considerable drumhead-like surface states
with unique connection patterns are illustrated to identify the non-trivial
band topology, which may be measured by future experiments.
