  Vertical heterostructures combining different layered materials offer novel
opportunities for applications and fundamental studies of collective behavior
driven by inter-layer Coulomb coupling. Here we report heterostructures
comprising a single-layer (or bilayer) graphene carrying a fluid of massless
(massive) chiral carriers, and a quantum well created in GaAs 31.5 nm below the
surface, supporting a high-mobility two-dimensional electron gas. These are a
new class of double-layer devices composed of spatially-separated electron and
hole fluids. We find that the Coulomb drag resistivity significantly increases
for temperatures below 5-10 K, following a logarithmic law. This anomalous
behavior is a signature of the onset of strong inter-layer correlations,
compatible with the formation of a condensate of permanent excitons. The
ability to induce strongly-correlated electron-hole states paves the way for
the realization of coherent circuits with minimal dissipation and nanodevices
including analog-to-digital converters and topologically protected quantum
bits.
