Quantum geometric excitations in fractional Chern insulators

Topological quantum fluids in partially filled Chern bands have rich dynamical properties emerging from the interplay between quantum geometry and universal topological properties. In Landau levels multiple graviton-like spin-2 geometric excitations can emerge from fractional quantum Hall phases [1], as the quantum geometric fluctuations of conformal Hilbert spaces. Such excitations have been recently detected in experiments (Nature 628, 78-83, 2024). We show geometric excitations can also help us understand the fundamental similarities and differences between Landau levels and generic Chern bands (e.g. from lattice models or moire systems). One can show with newly developed analytical tools the surprising emergence of “guiding center" continuous rotational invariance of the ground states and the geometric excitations with well-defined spins in moire systems, despite the explicit breaking of rotational symmetry. Nevertheless, such excitations generally have short lifetime (in contrast to finite size numerical computations) due to strong scattering by the anisotropic gapped excitations. We propose experimental tuning strategies to lower the graviton mode energy below the gapped continuum, and argue this is a necessary condition enabling the observation of graviton modes and geometric excitations in realistic moire systems [2,3].

[1] Yuzhu Wang and Bo Yang, Nat. Commun. 14, 2317 (2023)

[2] Yuzhu Wang, J. Huxford, DX. Nguyen, G. Ji, YB. Kim, Bo Yang, arXiv:2502.02640

[3] Bo Yang, arXiv: 2503.19017