Theory of excitonic topological order in imbalanced electron-hole bilayers

Correlation and frustration play essential roles in physics, which give rise to a variety of exotic quantum phases, e.g., the quantum spin-liquids. On the other hand, boson condensation is known to generate quantum state with macroscopic coherence such as superfluid. In semiconductors, it is well known that electrons and holes can form bosonic pairs, termed excitons, which can condense and form excitonic insulators. Then, a key question of great interest is that whether excitons can always condense at zero temperature, and is it possible for quantum spin-liquid like physics to emerge in excitonic systems under certain circumstances? We show that correlated electron-hole bilayers with density imbalance could support an excitonic topological order (ETO) in the phase diagram, which is a time-reversal breaking topological order with fractionalized excitations, akin to the fractional quantum Hall states. At microscopic level, the density imbalance leads to excess particles competing with the formed excitons, resulting in large degeneracy of exciton configurations, i.e., the frustration. The frustration is manifested in momentum space as a moat-like band (similar to flat band). The interacting excitons on moat band cannot condense. Instead, we show that the ETO emerges in certain parameter range with lower energy than all known boson condensation states. The ETO exhibits edge states consisting of a pair of chiral electron and hole channel. It well explains the recent experiments in InAs/GaSb quantum wells, in terms of the observed excitonic bulk gap under strong electron-hole density imbalance and the edge transport under both zero and high magnetic fields.