Higher spin modes in fractional quantum Hall fluids

Neutral excitations in a fractional quantum Hall droplet define the incompressibility gap of the topological phase, and some of them have been well understood in theory and probed in experiments. In this presentation, we would like to introduce an algebraic method to construct the model wave functions of a set of neutral excitations on a sphere, which also works for the graviton/magnetoroton modes and becomes more universal than the single mode approximation since it is not restricted to the small-wave-vector limit. More importantly, our method can generate the microscopic wave functions of higher spin modes with S=4, 6, 8… with their descendants, for both Abelian and non-Abelian phases. Furthermore, we find emergent supersymmetry between all the higher-spin modes in the neutral fermion sectors and the magnetoroton sectors in the Pfaffian phase. Surprisingly, one can construct well-defined wave functions of double-graviton (or even N-graviton) modes with our approach. All the higher-spin wave functions given by this approach have sharp and high resonance peaks in the spectral functions, implying that they are good model states. The theoretical and experimental relevance of these higher spin modes will be discussed.