Phonon spectra and lattice specific heats of the thallium-based high-temperature superconductors

We present the phonon-dispersion curves, the one-phonon densities of state, the lattice specific heat ${\mathit{c}}_{\mathit{v}}$(T), and the Debye temperatures FTHETA(T) of the thallium-based high-temperature superconductors, based on full lattice dynamical calculations. Repelling effects due to hybridization of the low-lying transverse acoustic and optical modes lead to small Debye regions of the specific heat (≤4 K), while the occurrence of low-lying dispersionless transverse modes in the outer parts of the Brillouin zone causes large drops in the Debye temperatures FTHETA(T) in the range 0 to 20 K. These effects are extremely pronounced in ${\mathrm{Tl}}_2$ ${\mathrm{Ca}}_2$ ${\mathrm{Ba}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{10}$ because of the appearance of very-low-frequency modes.