Symmetry breaking and fermionic fractional Chern insulator in topologically trivial bands

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 ${\rho }_{\mathrm{C}\mathrm{O}}=2\mathrm{/}3$ particles per site, then dope the model to higher densities $\rho = \rho_{$\mathrm{C}\mathrm{O}$} + \nu/6$\mathrm{.}At$\nu=1/3,2/5$($\rho=13/18,11/15$), we observe definitive signatures of both CO and the FQH effect — sharply peaked static structure factor, gapped and degenerate energy spectrum and fractionally quantized Hall conductivity ${\sigma }_{\mathrm{H}}=1\mathrm{/}3,2\mathrm{/}5$ in units of $e^2\mathrm{/}h$ — over a range of all model parameters. We thus obtain direct evidence for fermionic SBT order of FQH type in topologically trivial bands.