  The assembly of suitably designed van der Waals (vdW) heterostructures
represents a new approach to produce artificial systems with engineered
electronic properties. Here, we apply this strategy to realize synthetic
semimetals based on vdW interfaces formed by two different semiconductors.
Guided by existing ab-initio calculations, we select WSe$_2$ and SnSe$_2$ mono
and multilayers to assemble vdW interfaces, and demonstrate the occurrence of
semimetallicity by means of different transport experiments. Semimetallicity
manifests itself in a finite minimum conductance upon sweeping the gate over a
large range in ionic liquid gated devices, which also offer spectroscopic
capabilities enabling the quantitative determination of the band overlap. The
semimetallic state is additionally revealed in Hall effect measurements by the
coexistence of electrons and holes, observed by either looking at the evolution
of the Hall slope with sweeping the gate voltage or with lowering temperature.
Finally, semimetallicity results in the low-temperature metallic conductivity
of interfaces of two materials that are themselves insulating. These results
demonstrate the possibility to implement a state of matter that had not yet
been realized in vdW interfaces, and represent a first step towards using these
interfaces to engineer topological or excitonic insulating states.
