Nanoscale structural correlations in a model cuprate superconductor

Understanding the extent and role of inhomogeneity is a pivotal challenge in the physics of cuprate superconductors. While it is known that structural and electronic inhomogeneity is prevalent in the cuprates, it has proven difficult to disentangle compound-specific features from universally relevant effects. Here we combine advanced neutron and x-ray diffuse scattering with numerical modeling to obtain insight into bulk structural correlations in HgBa$_2$CuO$_{4+\delta}$. This cuprate exhibits a high optimal transition temperature of nearly 100 K, pristine charge-transport behavior, and a simple average crystal structure without long-range structural instabilities, and is therefore uniquely suited for investigations of intrinsic inhomogeneity. We uncover diffuse reciprocal-space patterns that correspond to prominent nanoscale correlations of atomic displacements perpendicular to the CuO$_2$ planes. The real-space nature of the correlations is revealed through three-dimensional pair distribution function analysis and complementary numerical refinement. We find that relative displacements of ionic and CuO$_2$ layers play a crucial role, and that the structural inhomogeneity is not directly caused by the presence of conventional point defects. The observed correlations are therefore intrinsic to HgBa$_2$CuO$_{4+\delta}$, and thus likely important for the physics of cuprates more broadly. It is possible that the structural correlations are closely related to the unusual superconducting correlations and Mott-localization in these complex oxides. As advances in scattering techniques yield increasingly comprehensive data, the experimental and analysis tools developed here for large volumes of diffuse scattering data can be expected to aid future investigations of a wide range of materials.