  Two-dimensional Weyl superconductor is the most elusive member of a group of
materials with Weyl fermions as low-energy excitations. Here, we propose to
realize this state in a heterostructure consisting of thin films of half-metal
and spin-singlet superconductor. In particular, for the $d$-wave case, a very
robust two-dimensional Weyl superconductor (dWSC) is realized independent of
the orientation of the spontaneous magnetization of the half-metal. The
quasiparticle spectra of the dWSC show interesting evolution with the direction
of the magnetization, featured by a series of Lifshitz transitions in the
zero-energy contour of the quasiparticle spectrum. For a general magnetization
orientation of the half-metal, the state is a combination of a superconducting
component and a normal fluid component and is different from all known forms of
pairings. In addition, we find a transition between type-I and type-II Weyl
nodes. This is also the first example of a type-II Weyl node in the presence of
superconducting correlation. The symmetries and topological properties of the
system are analyzed. We also study the phases in the heterostructure with the
half-metal replaced by a ferromagnetic metal with a partially spin-polarized
Fermi surface.
