  Synthesizing a polarizable environment surrounding a low-dimensional metal to
generate superconductivity is a simple theoretical idea that still awaits a
convincing experimental realization. The challenging requirements are satisfied
in a metallic bilayer when the ratio between the Fermi velocities is small and
both metals have a similar, low carrier density. In this case, the slower
electron gas acts as a retarded polarizable medium (a "dielectric" environment)
for the faster metal. Here we show that this concept is naturally optimized for
the case of an atomically thin bilayer consisting of a Dirac semimetal (e.g.
graphene) placed in atomic-scale proximity to a doped semiconducting transition
metal dichalcogenide (e.g. WSe$_2$). The superconducting transition temperature
that arises from the dynamically screened Coulomb repulsion is computed using
the linearized Eliashberg equation. In the case of graphene on WSe$_2$, we find
that $T_c$ can exceed 100 mK, and it increases further when the Dirac valley
degeneracy is reduced. Thus, we argue that suspended van der Waals bilayers are
in a unique position to realize experimentally this long anticipated
theoretical concept.
