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We study the temperature dependence of the low energy phonons in the $(H, 0,L)$ reciprocal plane of the highly ordered ortho-II YBa$_2$Cu$_3$O$_{6.55}$cuprate high temperature superconductor by means of high-resolution inelasticx-ray scattering. Anomalies associated with the emergence of long-range chargedensity wave (CDW) fluctuations are observed, and are qualitatively similar tothose previously observed in the $(0, K, L)$ plane. This confirms theunconventional nature of this bi-dimensional CDW, which is not soft-phonondriven. With the support of first principles calculations, the symmetry of theanomalous phonon is identified and is found to match that of the chargemodulation. This suggests in turn that these anomalies originate from a directcoupling between the phonons and the collective CDW excitations.

In-plane Isotropy of the Low Energy Phonon Anomalies in YBa$_{2}$Cu$_{3}$O$_{6+x}$