Graviton Chirality and Topological Order in the Half-filled Landau Level

Recent work[1] has established that fractional quantum Hall liquids support graviton-like excitations that carries definitive chirality. We apply this insight to the fractional quantum Hall state at Landau level (LL) filling factor ν = 5/2, which is extremely interesting because it is likely the first non-Abelian state, but its precise nature remains unclear after decades of study. We demonstrate this can be resolved by studying the chirality of its graviton excitations, using circularly polarized Raman scattering [2]. We also discuss the advantage of this bulk probe over the existing edge probes.