We describe a mechanism by which fermions in topologically trivial bands can form correlated states exhibiting a fractional quantum Hall (FQH) effect upon introduction of strong repulsive interactions. These states are solid-liquid composites, in which a FQH liquid is induced by the formation of charge order (CO), following a recently proposed paradigm of symmetry-breaking topological (SBT) order [Phys. Rev. Lett. 113, 216404 (2014)]. We devise a spinless fermion model on a triangular lattice, featuring a topologically trivial phase when interactions are omitted. Adding strong short-range repulsion, we first establish a repulsion-driven CO phase at density ${\rho }_{\mathrm{CO}}=2/3$ particles per site, then dope the model to higher densities $\rho ={\rho }_{\mathrm{CO}}+\nu /6$. At $\nu =1/3,2/5$ ($\rho =13/18,11/15$) we observe definitive signatures of both CO and the FQH effect—a sharply peaked static structure factor, gapped and degenerate energy spectrum, and fractionally quantized Hall conductivity ${\sigma }_{\mathrm{H}}=1/3,2/5$ in units of $e^2/h$—over a range of all model parameters. We thus obtain direct evidence for fermionic SBT order of FQH type in topologically trivial bands.

• Received 6 November 2017

DOI:https://doi.org/10.1103/PhysRevB.97.085108