We report high spatial resolution, below 100 nm, scanning nano x-ray diffraction (SnXRD) imaging of incommensurate lattice modulations (ILM) in ${\mathrm{Bi}}_{2.1}{\mathrm{Sr}}_{1.9}\mathrm{CaC}{\mathrm{u}}_{2.0}{\mathrm{O}}_{8+y}$ van der Waals 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.

中文翻译：

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原子薄的高温Bi2.1Sr1.9CaCu2.0O8 + y超导体中的空间相关不对称晶格调制

我们报告高空间分辨率，低于100 nm，扫描纳米X射线衍射（SnXRD）成像的不相称晶格调制（ILM）在 ${\mathrm{双}}_{2.1}{\mathrm{r}}_{1.9}\mathrm{碳酸钙}{\mathrm{ü}}_{2.0}{\mathrm{Ø}}_{8+ÿ}$范德华斯异质结构的厚度低至两个晶胞。我们揭示了散装样品中和表面上不同的远距离ILM。我们发现，ILM的水坑状域的大小和相互定向是由系统的维数决定的。在两单元样品中，长程和短程波矢量反相关，并且出现的空间模式具有方向梯度。这些出现的模式暗示静态介观晶格调制。我们的发现为局部应变工程调节二维高温超导体的特性开辟了一条途径。