Excitonic topological order in correlated electron-hole bilayers

Correlation and frustration play essential roles in physics, which gives rise to a variety of exotic quantum phases. We have observed an unconventional excitonic ground state with unequal electron and hole densities in inverted InAs/GaSb bilayers. Here in zero magnetic field (B) a large bulk gap exists encompassing a broad range of density imbalance, accompanied by a gapless edge state that resembles helical transport. Under an increasing perpendicular B the bulk gap persists in the same regime and anomalous plateau of Hall signal appears, demonstrating an evolution from helical-like to chiral-like edge transport. These results point to a spontaneous time-reversal symmetry (TRS) breaking topological excitonic insulator with density imbalance. Theoretically, we find that, strong frustration from density imbalance leads to a moat band for excitons (similar to a flat band). This generates an excitonic topological order (ETO) which can be represented by a composite fermion (a boson attached to one Chern-Simons flux) state at filling factor 1. The ETO consistently explains all our experimental observations. Our work could open up a new direction for research on topological and correlated bosonic system in solid states.