Spatially correlated incommensurate lattice modulations in an atomically thin high-temperature Bi2.1Sr1.9CaCu2.0O8+y superconductor

We report high spatial resolution, below 100 nm, scanning nano x-ray diffraction (SnXRD) imaging of incommensurate lattice modulations (ILM) in Bi2.1Sr1.9CaCu2.0O8+y van derWaals heterostructures of thicknesses down to two unit cells. We reveal the distinct long-range and short-range ILMs in a bulk sample and at the surface. We find that the size and mutual orientation of the puddlelike domains of the ILM are determined by the dimensionality of the system. In the two-unit-cell sample, the wave vectors of the long- and short-range orders become anticorrelated, and the emergent spatial patterns have a directional gradient. These emergent patterns imply static mesoscopic lattice modulation. Our findings open a route for local strain engineering to modulate properties of two-dimensional high-temperature superconductors.