  Excitonic insulators (EI) arise from the formation of bound electron-hole
pairs (excitons) in semiconductors and provide a solid-state platform for
quantum many-boson physics. Strong exciton-exciton repulsion is expected to
stabilize condensed superfluid and crystalline phases by suppressing both
density and phase fluctuations. Although spectroscopic signatures of EIs have
been reported, conclusive evidence for strongly correlated EI states has
remained elusive. Here, we demonstrate a strongly correlated spatially indirect
two-dimensional (2D) EI ground state formed in transition metal dichalcogenide
(TMD) semiconductor double layers. An equilibrium interlayer exciton fluid is
formed when the bias voltage applied between the two electrically isolated TMD
layers, is tuned to a range that populates bound electron-hole pairs, but not
free electrons or holes. Capacitance measurements show that the fluid is
exciton-compressible but charge-incompressible - direct thermodynamic evidence
of the EI. The fluid is also strongly correlated with a dimensionless exciton
coupling constant exceeding 10. We further construct an exciton phase diagram
that reveals both the Mott transition and interaction-stabilized
quasi-condensation. Our experiment paves the path for realizing the exotic
quantum phases of excitons, as well as multi-terminal exciton circuitry for
applications.

Materials Science;Mesoscale and Nanoscale Physics;Strongly Correlated Electrons