Abstract

The formation of fractional quantum-Hall (FQH) states in lattice systems without externally applied magnetic fields—dubbed fractional Chern insulators (FCI)—is a recent and promising theoretical proposal that has the potential to render the FQH effect experimentally more accessible. The paradigmatic FCIs are found when interacting electrons with frozen spin degree of freedom populate relatively flat topological bands, with the interaction strength being smaller than the gap to other bands. In this talk, I will show that this limit is adiabatically connected to the opposite one, in which the interaction strength goes to infinity, thus exceeding the gap to other bands. Electrons then become extended hard-core particles, the notion of bands becomes meaningless and the connection to Landau level physics of the fractional quantum-Hall effect is much less obvious. FCI states are very robust in this hardcore limit, reaching up to, or possibly beyond, the non-interacting topological phase transition. Strong interactions may also give rise to competition between topological and conventional charge order. After discussing this competition, I will introduce a class of states in which the FCI topological order is induced by the presence of a charge-density wave and will present numerical evidence for this coexistence. Finally, based on these compositely ordered states, I will provide a recipe for topological order out of a topologically trivial band structure.