Phonon anomalies in trilayer high-Tc superconductors

We present an extension of the model proposed recently to account for dramatic changes below Tc (anomalies) of some c-axis polarized infrared-active phonons in bilayer cuprate superconductors, that applies to trilayer high-Tc compounds. We discuss several types of phonon anomalies that can occur in these systems and demonstrate that our model is capable of explaining the spectral changes occurring upon entering the superconducting state in the trilayer compound Tl2Ba2Ca2Cu3O10. The low-temperature spectra of this compound obtained by Zetterer and coworkers display an additional broad absorption band, similar to the one observed in underdoped YBa2Cu3O7-delta and Bi2Sr2CaCu2O8. In addition, three phonon modes are strongly anomalous. We attribute the absorption band to the transverse Josephson plasma resonance, similar to that of the bilayer compounds. The phonon anomalies are shown to result from a modification of the local fields induced by the formation of the resonance. The spectral changes in Tl2Ba2Ca2Cu3O10 are compared with those occurring in Bi2Sr2Ca2Cu3O10, reported recently by Boris and coworkers.