A Structural Probe of the Doped Holes in Cuprate Superconductors

An unresolved issue concerning cuprate superconductors is whether the distribution of carriers in the CuO2 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 La2CuO4+delta (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 x 10(-7) electrons, suggesting an absence of in-plane hole ordering in this material.