Lattice dynamics of high-Tcsuperconductors: Optical modes of the thallium-based compounds

We present a lattice-dynamical calculation of the Raman- and infrared-active modes of the following six thallium-based high-${\mathit{T}}_{\mathit{c}}$ superconductors: ${\mathrm{Tl}}_2$ ${\mathrm{Ba}}_2$ ${\mathrm{CuO}}_6$, ${\mathrm{Tl}}_2$ ${\mathrm{CaBa}}_2$ ${\mathrm{Cu}}_2$ ${\mathrm{O}}_8$, and ${\mathrm{Tl}}_2$ ${\mathrm{Ca}}_2$ ${\mathrm{Ba}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{10}$ (body-centered-tetragonal structures) and ${\mathrm{TlCaBa}}_2$ ${\mathrm{Cu}}_2$ ${\mathrm{O}}_7$, ${\mathrm{TlCa}}_2$ ${\mathrm{Ba}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_9$, and ${\mathrm{TlCa}}_3$ ${\mathrm{Ba}}_2$ ${\mathrm{Cu}}_4$ ${\mathrm{O}}_{11}$ (simple-tetragonal structures). Our calculations are based on a shell model that incorporates short-range overlap potentials, long-range Coulomb potentials, and ionic polarizabilities. We also require that the shell models for different high-${\mathit{T}}_{\mathit{c}}$ superconducting compounds be mutually compatible, namely that the short-range potentials for given ion pairs in equivalent environments be transferable from one compound to the other. The model presented here does in fact utilize a common set of short-range potentials that apply to the entire series of thallium-based superconductors as well as to ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_7$ and ${\mathrm{Bi}}_2$ ${\mathrm{CaSr}}_2$