Learning hidden structure of nanoscale spectroscopies with metric analysis

Scanning probe microscopy is routinely faced with analysis of heterogeneous datasets, largely without having reference analytical models. Ordered parts of probed materials, such as regular lattice structures or coherent scattering can often be effectively captured with integral transforms to reveal the atomic and electronic structure, sometimes with unprecedented resolution. However, the problem of capturing inhomogeneities and furthermore understanding of their physical significance demands further attention. Here we will demonstrate how an appropriately chosen metric, combined with analysis of its variability enables effective characterization of key and often hidden structures within hyperspectral datasets. We applied such methodology to three representative cases with remarkably strong inhomogeneity in the nanoscale properties – variability of superconducting gap and electronic structure in unconventional superconductors FeSe and Ba₂FeAs₂, measurement of individual defects in these systems and structural phase transitions in dipolar solids. In each case, metric analysis has revealed a wide-range of sometimes unexpected properties, such as log-normal distribution in tunneling spectroscopy and sub-surface location of atomic-scale defects, while also providing a robust approach to understand spectral weight transfer and spectral signatures of electronic defects and to detect phase transitions in dielectric solids from their hysteretic response to applied fields. Future extension of these methodologies to combine elements of machine and deep learning will also be discussed.