石墨烯的数据挖掘：含缺陷单分子膜结构与电子自由度的相关分析
Data Mining Graphene: Correlative Analysis of Structure and Electronic Degrees of Freedom in Graphenic Monolayers with Defects
摘要：
材料晶体结构的变化与其机械、电子、磁性和光学功能之间的联系-称为结构-性质关系-是当代材料科学研究的基石。扫描透射电子显微镜和扫描探针显微镜（STEM和SPM）的最新进展为在单杂质和原子构型水平上研究材料的结构-性能关系开辟了一条前所未有的道路。然而，缺乏的是基于几何学的方法，在STEM和SPM实验的不同信息通道中获得的结构和属性变量的互相关。在这里，我们设计了一种基于滑动窗口快速傅里叶变换，皮尔逊相关矩阵，线性和核正则相关的组合的方法，研究晶格畸变和电子散射之间的关系，从SPM数据石墨烯缺陷。我们的分析表明，应变耦合的强度在不同的散射通道之间发生变化，这可以解释在感兴趣的纳米尺度区域中共存的几种准粒子干涉图案。此外，核函数的应用允许我们提取石墨烯中的晶格应变和散射强度之间的关系的非线性分量。所概述的方法可以进一步用于分析各种多模态成像技术中的相关性，其中感兴趣的信息在空间上分布并且通常具有复杂的多维性质。
英文摘要：
The link between changes in the material crystal structure and its mechanical, electronic, magnetic, and optical functionalities - known as the structure-property relationship - is the cornerstone of the contemporary materials science research. The recent advances in scanning transmission electron and scanning probe microscopies (STEM and SPM) have opened an unprecedented path towards examining the materials structure-property relationships on the single-impurity and atomic-configuration levels. Lacking, however, are the statistics-based approaches for cross-correlation of structure and property variables obtained in different information channels of the STEM and SPM experiments. Here we have designed an approach based on a combination of sliding window fast Fourier transform, Pearson correlation matrix, and linear and kernel canonical correlation, to study a relationship between lattice distortions and electron scattering from SPM data on graphene with defects. Our analysis revealed that the strength of coupling to strain is altered between different scattering channels, which can explain coexistence of several quasiparticle interference patterns in nanoscale regions of interest. In addition, the application of kernel functions allowed us to extract a non-linear component of the relationship between the lattice strain and scattering intensity in graphene. The outlined approach can be further utilized towards analyzing correlations in various multi-modal imaging techniques where the information of interest is spatially distributed and generally has a complex multidimensional nature.
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