  Chiral topological orders formed in correlated fermion systems have been
widely explored. However, the mechanism on how they emerge from interacting
fermions is still unclear. Here, we propose a susceptibility condition. Under
this condition, we show that chiral topological orders can spontaneously take
place in correlated fermion systems. The condition leads to a low-energy
effective theory of bosons with strong frustration, mimicking the flat band
systems. The frustration then melts the long-range orders and results in
topological orders with time-reversal symmetry breaking. We apply the theory to
strongly-correlated semiconductors doped to the metallic phase. A novel
excitonic topological order with semionic excitations and chiral excitonic edge
state is revealed. We also discuss the application to frustrated magnets. The
theory predicts a chiral spin liquid state, which is numerically confirmed by
our tensor network calculations. These results demonstrate an unprecedented
indicator for chiral topological orders, which bridges the existing gap between
interacting fermions and correlated topological matter.
