A Structural Probe of the Doped Holes in Cuprate Superconductors

An unresolved issue concerning cuprate superconductors is whether the distribution of carriers in the CuO 2 plane is uniform or inhomogeneous. Because the carriers comprise a small fraction of the total charge density and may be rapidly fluctuating, modulations are difficult to detect directly. We demonstrate that in anomalous x-ray scattering at the oxygen K edge of the cuprates, the contribution of carriers to the scattering amplitude is selectively magnified 82 times. This enhances diffraction from the doped holes by more than 10 3 , permitting direct structural analysis of the superconducting ground state. Scattering from thin films of La 2 CuO 4+δ (superconducting transition temperature = 39 K) at temperature = 50 ± 5 kelvin on the reciprocal space intervals (0,0,0.21) → (0,0,1.21) and (0,0,0.6) → (0.3,0,0.6) shows a rounding of the carrier density near the substrate suggestive of a depletion zone or similar effect. The structure factor for off-specular scattering was less than 3 × 10 −7 electrons, suggesting an absence of in-plane hole ordering in this material.