Phonon anomalies and lattice dynamics in superconducting oxychlorides Ca$_{2-x}$CuO$_2$Cl
Résumé
We present a comprehensive study of the phonon dispersion in an underdoped, superconducting Ca$_{2-x}$CuO$_2$Cl$_2$ crystal. We interpret the results using lattice dynamical calculations based on a shell model, and we compare the results, to other hole-doped cuprates, in particular to the ones isomorphic to LSCO. We found that an anomalous dip in the Cu-O bond stretching dispersion develops in oxychlorides with a simultaneous marked broadening of the mode. The broadening maximum appear at $\approx (\pi / (2a) ~ 0 ~ 0)$ that corresponds to the charge-modulations propagation vector. Our analysis also suggests that screening effects in calculations may cause an apparent cosine-shaped bending of the Cu-O bond-stretching dispersion along both the ($q$ 0 0) and the ($q$ $q$ 0) directions, that is not observed on the data close to optimal doping. This observation suggests that the discrepancy between experimental data and \textit{ab-initio} calculations on this mode originates from an overestimation of the doping effects on the mode.
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