Theory of Raman scattering in Mott-Hubbard systems

Abstract

We present a theory of Raman scattering in the Hubbard model. The scattering of light has two contributions. One gives rise to scattering by spin degrees of freedom in the insulating case where the general form of the scattering Hamiltonian is derived. The fluctuations of the ‘‘chiral’’ spin operator ${\mathrm{\Sigma }}_{{\mathit{S}}_{\mathit{i}}}$⋅(${\mathrm{S}}_{\mathit{i}}$×${\mathrm{S}}_{\mathit{k}}$) are shown to contribute in the ${\mathit{B}}_{2\mathit{g}}$ scattering geometry. The other contributes 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 to density fluctuations in usual metals.