Raman Scattering in Mott-Hubbard Systems

We present a theory of Raman Scattering in the Hubbard model. The scattering of light has resonant and non-resonant contributions. The resonant term gives rise to scattering by spin degrees of freedom in the insulating case, for which we derive a general form of the effective scattering Hamiltonian. The later involves four terms with distinct symmetry properties, one of them being the “chiral” spin operator ∑ Si · (Sj×Sk). The corresponding four distinct correlation function can be measured directly in the experiments with different scattering geometries. The nonresonant term contributes to the scattering in the doped case and is shown to probe the fluctuations of the “stress tensor”. This quantity is not conserved and hence its fluctuations at small q inherent in optical experiments, need not be small, in striking contrast with the density fluctuation in usual metals.