PHONON-DISPERSION, PHONON SPECIFIC-HEAT, AND DEBYE TEMPERATURE OF HIGH-TEMPERATURE SUPERCONDUCTORS

A simple model representing the low-frequency acoustical and optical modes of the high-temperature superconductors (HTSC's) leads to a surprisingly realistic representation of the low-temperature specific heats c(upsilon)(T) and the corresponding Debye temperatures THETA(T) of the HTSC'S. The model allows us to relate the characteristics and peculiarities of c(upsilon)(T) and THETA(T) directly to various features of the low-frequency phonon dispersion, and it is found that c(upsilon) and THETA can exhibit rather well the identifiable features of phonon anomalies. For instance, a surprising result is that optic Einstein-like modes at nu(E) = 2 THz (hnu(E)/k(B) = 96 K) in our model begin to have an effect at 6 K. This behavior has potentially important consequences for the procedure of separating the phonon contribution from the measured specific heat, in order to obtain the nonphonon specific-heat contributions. Another consequence of the occurrence of these Einstein modes is the presence of low-frequency phonons with large wave vectors, which means that umklapp scattering can begin to play a role at temperatures lower than usually assumed. This, in tum, may require a modification of the customary qualitative picture of the low-temperature electrical and thermal conductivities.