Systematics of c -axis phonons in the thallium- and bismuth-based cuprate superconductors

We present grazing incidence reflectivity measurements in the far-infrared region at temperatures above and below Tc for a series of thallium- (Tl₂Ba₂CuO₆, Tl₂Ba₂CaCu₂O₈) and bismuth- (Bi₂Sr₂CuO₆, Bi₂Sr₂CaCu₂O₈, and Bi_2-xPbₓSr₂CaCu₂O₈) based cuprate superconductors. From the spectra, which are dominated by the c-axis phonons, longitudinal optical (LO) frequencies are directly obtained. The reflectivity curves are well fitted by a series of Lorentz oscillators. In this way the transverse optical (TO) phonon frequencies were accurately determined. On the basis of the comparative study of the Bi- and Tl-based cuprates with a different number of CuO₂ layers per unit cell, we suggest modifications of the assignment of the main oxygen modes. We compare the LO frequencies in Bi₂Sr₂CaCu₂O₈ and Tl₂Ba₂Ca₂Cu₃O₁₀ obtained from intrinsic Josephson junction characteristics with our measurements, and explain the discrepancy in LO frequencies obtained by the two different methods.