Phase diagram at filling fraction ν=2/3

Determine the phase diagram of the Aharonov–Casher band at filling fraction ν=2/3, including the competition among fractional Chern insulators, re-entrant integer quantum anomalous Hall states, possible superconductivity, and other competing phases.

Background

The paper focuses primarily on fractional fillings ν=1/3, 1/7, and 1/9 and analyzes the competition between Laughlin-like liquids and generalized Wigner crystals. The authors note that experiments near ν=2/3 exhibit a richer set of phases, including fractional Chern insulators, re-entrant integer quantum anomalous Hall states, and possible superconductivity.

Related numerical studies suggest that superconductivity may occur near ν=2/3 in Aharonov–Casher bands and related models, but the full phase structure at this filling is not analyzed in the paper. A systematic phase-diagram study is therefore left unresolved.