Mechanism to soften the graviton mode in FQAH states

Identify interaction mechanisms or band-geometry conditions that soften the graviton (geometric) collective mode in fractional quantum anomalous Hall states realized in lattice flat Chern bands, enabling neutral-mode softening without closing the charge gap.

Background

Softening of the graviton mode in Landau-level fractional quantum Hall systems can drive nematic phases with preserved translation symmetry. The present work demonstrates roton-driven translation-symmetry breaking within FQAH states but does not address graviton softening in lattice-based FQAH systems.

Understanding how to achieve graviton-mode softening in FQAH states would clarify routes to nematic phases and related critical phenomena in zero-magnetic-field lattice realizations.