Anomalous Expansion of the Copper-Apical Oxygen Distance in Superconducting La${}_2$CuO${}_4$ - La${}_{1.55}$Sr${}_{0.45}$CuO${}_4$ Bilayers

We have introduced an improved X-ray phase-retrieval method with unprecedented speed of convergence and precision, and used it to determine with sub-{\AA}ngstrom resolution the complete atomic structure of an ultrathin superconducting bilayer film, composed of La${}_{1.55}$Sr${}_{0.45}$CuO${}_4$ and La${}_2$CuO${}_4$ neither of which is superconducting by itself. The results show that phase-retrieval diffraction techniques enable accurate measurement of structural modifications in near-surface layers, which may be critically important for elucidation of surface-sensitive experiments. Specifically we find that close to the sample surface the unit cell size remains constant while the copper-apical oxygen distance shows a dramatic increase, by as much as 0.45 {\AA}. The apical oxygen displacement is known to have a profound effect on the superconducting transition temperature.