Systematics of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>c</mml:mi></mml:math>-axis phonons in the thallium- and bismuth-based cuprate superconductors

Abstract

We present grazing incidence reflectivity measurements in the far-infrared region at temperatures above and below ${T}_{c}$ for a series of thallium- $({\mathrm{Tl}}_{2}{\mathrm{Ba}}_{2}{\mathrm{CuO}}_{6},$ ${\mathrm{Tl}}_{2}{\mathrm{Ba}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8})$ and bismuth- $({\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CuO}}_{6},$ ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8},$ and ${\mathrm{Bi}}_{2\ensuremath{-}x}{\mathrm{Pb}}_{x}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8})$ 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 ${\mathrm{CuO}}_{2}$ layers per unit cell, we suggest modifications of the assignment of the main oxygen modes. We compare the LO frequencies in ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8}$ and ${\mathrm{Tl}}_{2}{\mathrm{Ba}}_{2}{\mathrm{Ca}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{10}$ obtained from intrinsic Josephson junction characteristics with our measurements, and explain the discrepancy in LO frequencies obtained by the two different methods.