Dynamics and lifetime of geometric excitations in moiré systems

Abstract

Recently observed spin-2 collective excitations, known as chiral graviton modes, encode noncommutative geometry and topological information in fractional quantum Hall systems. An outstanding question is whether such chiral geometric excitations remain well-defined in moiré Chern bands hosting fractional Chern insulator phases, where continuous rotational symmetry is explicitly broken. Combining extensive numerical simulations with analytical tools, we demonstrate that graviton modes with well-defined chirality can persist in moiré Chern bands. Remarkably, their existence is enabled by an emergent restoration of full rotational symmetry in the many-body ground state. This establishes fractional Chern insulators as a promising platform for probing geometric collective modes beyond Landau levels. We further uncover an important subtlety: in generic Chern bands, the lack of continuous rotational symmetry for gapped excitations enhances scattering and suppresses graviton lifetimes in the thermodynamic limit. Nonetheless, we propose tuning strategies that stabilize graviton modes by lowering their energies below the excitation continuum. Our results reveal novel phenomena unique to Chern bands and provide a concrete roadmap for experimentally accessing geometric collective excitations in moiré materials.