利用扫描隧道显微镜中的局域波矢映射应变与空间调制相位

中文摘要 AI 辅助

空间变化的晶格畸变可导致电子性质的局域变化，而这些变化常被对扩展区域进行平均的测量所掩盖。凭借其原子尺度的空间分辨率，扫描隧道显微镜（STM）原则上提供了一种在局域范围内量化此类畸变的手段。从STM图像中提取局域应变的一种广泛使用的方法是Lawler-Fujita（LF）算法[Lawler等人，Nature 466, 347 (2010)]，该算法从晶格调制的相位确定位移场，随后通过微分获得应变。然而，这种方法需要二维相位展开，这在相位定义不明确的区域（特别是靠近诸如刃型位错等拓扑缺陷处）可能会失败。在此，我们引入一种替代方法，通过在实空间中直接测量局域波矢来规避这些限制。我们推导了局域波矢、应变和相位梯度之间的关系，并表明即使在相位本身定义不明确的情况下，局域波矢映射（LWM）算法仍然稳健。这使得该方法特别适用于对与涡旋及其他拓扑缺陷相关的相位梯度纹理进行成像。我们使用包含已知晶格畸变和人工生成涡旋的模拟数据对该算法进行了基准测试。最后，我们将该方法应用于实验STM数据，解析了4Ha-NbSe2和2H-NbSe2中的电荷密度波（CDW）不相称性、晶格畸变和CDW相位涡旋。这些观测的物理意义最近由S. Sajan、X. Yang等人报道[arXiv:2607.20335 (2026)]。程序包及示例用法已在GitHub上公开：此https URL。

英文摘要

Spatially varying lattice distortions can produce local changes in electronic properties that are obscured by measurements averaging over extended regions. With its atomic-scale spatial resolution, scanning tunneling microscopy (STM) provides, in principle, a means of quantifying such distortions locally. A widely used approach for extracting local strain from STM images is the Lawler--Fujita (LF) algorithm [Lawler et al., Nature 466, 347 (2010)], which determines the displacement field from the phase of the lattice modulation and subsequently obtains the strain by differentiation. However, this approach requires two-dimensional phase unwrapping, which can fail in regions where the phase is ill-defined, particularly near topological defects such as edge dislocations. Here, we introduce an alternative approach that circumvents these limitations by directly measuring the local wave vector in real space. We derive the relationship between the local wave vector, strain, and the phase gradient, and show that the local wave vector mapping (LWM) algorithm remains robust even when the phase itself is ill-defined. This makes the method particularly well suited for imaging the phase-gradient textures associated with vortices and other topological defects. We benchmark the algorithm using simulated data containing known lattice distortions and artificially generated vortices. Finally, we apply the method to experimental STM data and resolve the charge density wave (CDW) incommensurabilities, lattice distortions, and CDW phase vortices in 4Ha-NbSe2 and 2H-NbSe2. The physical implications of these observations were recently reported by S. Sajan, X. Yang, et al. [arXiv:2607.20335 (2026)]. The program package and the example usage is publicly available at the GitHub: https://github.com/jsntxyang/LocalWavevectorMeasuremnt.

发表机构

• Yale University（耶鲁大学）
• Donostia International Physics Center（多诺斯蒂亚国际物理中心）
• Ikerbasque, Basque Foundation for Science（伊克尔巴斯克科学基金会）
• Centro de Física de Materiales CSIC-UPV/EHU（材料物理中心（CSIC-UPV/EHU））

机构由 AI 辅助整理，请以论文原文为准。