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

Abstract

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 (\ensuremath{\le}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.