Charge leakage in superconducting $\rm La_{2}CuO_{4}-La_{2-x}Sr_{x}CuO_{4}$ superlattices

Ability of grow crystalline high-temperature superconductor (HTS) superlattices using molecular beam epitaxy has opened new avenues of research. Scanning tunneling microscopy measurements have identified a pronounced influence of the dopant atoms on microscopic properties of bulk HTS, therefore raising the question of whether the holes can be spatially separated in an oxide heterostructure from the disordered doped layers in a way analogous to semiconductor modulation doping. We used resonant soft x-ray scattering (RSXS) to answer this question for $\rm La_{2}CuO_{4}-La_{2-x}Sr_{x}CuO_{4}$ superlattices. For a $\rm 15\times [2\times LCO-4\times LSCO]$ superlattice with x=0.36, the measured hole amplitude modulation at the O $K$ edge shows a relatively weak localization of the doped holes to the LSCO layers. By using the interference between ``structural" and resonant scattering at the Cu $L_{3}$ edge, the c-axis stress of the LSCO sublattice was also observed.