  Correlation and frustration play essential roles in physics, giving rise to
novel quantum phases [1-6]. A typical frustrated system is correlated bosons on
moat bands, which could host topological orders with long-range quantum
entanglement [4]. However, the realization of moat-band physics is still
challenging. Here, we explore moat-band phenomena in shallowly-inverted
InAs/GaSb quantum wells, where we observe an unconventional
time-reversal-symmetry breaking excitonic ground state under imbalanced
electron and hole densities. We find a large bulk gap exists encompassing a
broad range of density imbalance at zero magnetic field (B), accompanied by
edge channels that resemble helical transport. Under an increasing
perpendicular B, the bulk gap persists, and an anomalous plateau of Hall
signals appears, which demonstrates an evolution from helical-like to
chiral-like edge transport with a Hall conductance ~e2/h at 35 Tesla.
Theoretically, we show that strong frustration from density imbalance leads to
a moat band for excitons, resulting in a time-reversal-symmetry breaking
excitonic topological order, which explains all our experimental observations.
Our work opens up a new direction for research on topological and correlated
bosonic systems in solid states beyond the framework of symmetry-protected
topological phases, including but not limited to the bosonic fractional quantum
Hall effect.
