Separation dynamics of the resonant soft X-ray radiation into luminescence and coherent Raman scattering in wide gap insulators

Abstract

Abstract We study theoretically the roles of phonons in spectral shapes of soft X-ray radiation from a valence band to a core level in an insulator, and clarify how this radiation separates into luminescence and Raman scattering. We take a three-band system composed of a dispersionless core band, a conduction band, and a valence band, with wide energy gaps between them. Phonons with finite dispersion are assumed to couple weakly with a hole in the core band (core hole). Using this model, we calculate the resonant second order optical process composed of an excitation of an electron from the core band to the conduction band by an incident X-ray, and subsequent transition from the valence band to the core band by radiating another X-ray. Without phonons, the momentum of the core hole is expected to be well defined by the resonance condition of the incident X-ray. However, this momentum is dissipated by the phonons. If the radiation occurs after this dissipation, we get so-called luminescence which is independent of the incident X-ray. In this case, the spectral shape fully reflects the density of states (DOS) of the valence band. If the radiation occurs before the dissipation, we get resonant Raman scattering which depends on the incident X-ray. The spectral shape of this Raman scattering has a sharp peak, being quite different from the DOS. The relative intensity between these two components is determined by phonon dispersion, the life time of the core hole, and the core-hole–phonon coupling constant. From this theoretical framework, we have concluded that various cases exist—Raman dominant, luminescence dominant and intermediate—which is in good agreement with observations in recent experiments.