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.

References

A detailed investigation of the AC band phase diagram at $\nu=2/3$ is left for future work.

— Non-uniform quantum geometry stabilizes generalized Wigner crystals  (2609.04149 - Morales-Durán et al., 3 Sep 2026) in Discussion section

Before the neutral gap forms, pairing is marginal or irrelevant for repulsive inter-edge coupling unless an attractive neutral coupling favors its channel (Sec.~\ref{sec:coulomb}), so whether a pairing region gaps its neutral sector at realistic couplings is the main open problem; it requires treating the charge and neutral couplings together, beyond tree level.

— Parafermions in fractional Chern insulator-superconductor heterostructures: the role of spin polarization  (2610.01486 - Amire, 1 Oct 2026) in Section Open questions, immediately before Section 6