c -axis lattice dynamics in Bi-based cuprate superconductors

We present the results of a systematic study of the c-axis lattice dynamics in single-layer Bi₂Sr₂CuO₆ (Bi2201), bilayer Bi₂Sr₂CaCu₂O₈ (Bi2212), and trilayer Bi₂Sr₂Ca₂Cu₃O₁₀ (Bi2223) cuprate superconductors. Our study is based on both experimental data obtained by spectral ellipsometry on single crystals and theoretical calculations. The calculations are carried out within the framework of a classical shell model, which includes long-range Coulomb interactions and short-range interactions of the Buckingham form in a system of polarizable ions. Using the same set of shell model parameters for Bi2201, Bi2212, and Bi2223, we calculate the frequencies of the Brillouin-zone center phonon modes of A₂ᵤ symmetry and suggest the phonon mode eigenvector patterns. We achieve good agreement between the calculated A₂ᵤ eigenfrequencies and the experimental values of the c-axis TO phonon frequencies which allows us to make a reliable phonon mode assignment for all three Bi-based cuprate superconductors. We also present the results of our shell model calculations for the Γ-point A1g symmetry modes in Bi2201, Bi2212, and Bi2223 and suggest an assignment that is based on published experimental Raman spectra. The superconductivity-induced phonon anomalies recently observed in the c-axis infrared and resonant Raman scattering spectra in trilayer Bi2223 are consistently explained with the suggested assignment.