Chiral topological orders formed in correlated fermion systems have been widely explored. However, the mechanism of 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 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. An excitonic topological order with semionic excitations and a 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 indicator for chiral topological orders, which bridges the existing gap between interacting fermions and correlated topological matter.

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• Flat bands
• Topological order
• Strongly correlated systems
• Two-dimensional electron system
• Chern-Simons gauge theory
• Effective field theory
• Fermi liquid theory