Hierarchy of fractional Chern insulators and competing compressible states

Understand

We study the phase diagram of interacting electrons in a dispersionless Chern band as a function of their filling.

• We find hierarchy multiplets of incompressible states at fillings \nu=1/3, 2/5, 3/7, 4/9, 5/9, 4/7, 3/5 as well as \nu=1/5,2/7.
• These are accounted for by an analogy to Haldane pseudopotentials extracted from an analysis of the two-particle problem.
• Important distinctions to standard fractional quantum Hall physics are striking: absent particle-hole symmetry in a single band, an interaction-induced single-hole dispersion appears, which perturbs and eventually destabilizes incompressible states as \nu increases.