Data mining graphene: Correlative analysis of structure and electronic degrees of freedom in graphenic monolayers with defects

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 modern 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 structure-property relationships of materials at the single-impurity and atomic-configuration levels. However, there are no statistics-based approaches for cross-correlation of structure and property variables obtained from the different information channels of 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 methods to study the 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 the 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 used to analyze correlations in various multi-modal imaging techniques where the information of interest is spatially distributed and generally has a complex multi-dimensional nature.