Hierarchy of fractional Chern insulators and competing compressible states

TL;DR

This paper explores the phase diagram of interacting electrons in a Chern band, revealing a hierarchy of fractional Chern insulator states and their competition with compressible states, highlighting differences from traditional quantum Hall systems.

Contribution

It identifies a hierarchy of fractional Chern insulator states and analyzes their stability, introducing an analogy to Haldane pseudopotentials and revealing unique effects due to particle-hole asymmetry.

Findings

Hierarchy of incompressible states at various fillings

Absence of particle-hole symmetry impacts state stability

Interaction-induced single-hole dispersion destabilizes some states

Abstract

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. For this reason the nature of the state at \nu=2/3 is hard to pin down, while \nu=5/7,4/5 do not seem to be incompressible in our system.