Resonant Raman scattering in the superconducting cuprates: Frozen-phonon versus perturbational approach

We consider in detail Raman scattering by vibration of the apical oxygen ions in the RBa₂Cu₃O₇ superconducting cuprates. The scattering intensity is very sensitive to the ratio of diagonal and off-diagonal matrix elements of electron-phonon coupling, bandstructure, and carrier concentration. Our results show a large quantitative difference between the results of frozen-phonon and perturbational approach to the Raman process. The discrepancy becomes especially large when interband transitions to the states near the Fermi level are close to resonance with the incident light. The calculation of phonon-induced ion charge fluctuations shows an analogous discrepancy. The reason for these effects is the possibility of carrier redistribution between different parts of the Fermi surface arising in the frozen-phonon approximation. Our results show that Raman scattering in superconducting superlattices is very sensitive to the properties of the states near the Fermi level. For this reason experiments performed on the superlattices can help to resolve the discrepancy. Received 8 December 1999