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All underdoped high-temperature cuprate superconductors appear to exhibitcharge density wave (CDW) order, but both the underlying symmetry breaking andthe origin of the CDW remain unclear. We use X-ray diffraction to determine themicroscopic structure of the CDW in an archetypical cuprateYBa$_2$Cu$_3$O$_{6.54}$ at its superconducting transition temperature Tc ~ 60K. We find that the CDWs present in this material break the mirror symmetry ofthe CuO2 bilayers. The ionic displacements in a CDW have two components: oneperpendicular to the CuO$_2$ planes, and another parallel to these planes,which is out of phase with the first. The largest displacements are those ofthe planar oxygen atoms and are perpendicular to the CuO$_2$ planes. Ourresults allow many electronic properties of the underdoped cuprates to beunderstood. For instance, the CDW will lead to local variations in the doping(or electronic structure) giving an explicit explanation of the appearance ofdensity-wave states with broken symmetry in scanning tunnelling microscopy(STM) and soft X-ray measurements.

The nature of the charge density waves in under-doped YBa$_2$Cu$_3$O$_{6.54}$ revealed by X-ray measurements of the ionic displacements