Microscopic theory of higher-spin excitations in fractional quantum Hall fluids

We construct model wave functions for neutral excitations with spin $ S \ge 2$ in both abelian and non-abelian fractional quantum Hall phases on a sphere. We use the highest-weight condition to define these higher-spin states and study their dipole or quadrupole moment and lifetimes uniquely. They are the collective excitations emerging from generic non-area-preserving metric deformations, as a generalization of graviton modes. Interestingly, these modes get close to the graviton mode in the thermodynamic limit, which may provide one evidence for why the graviton modes can be stable and thus observed in experiments. Furthermore, we proposed feasible experimental approaches to observe the higher spin modes.