Learning from disorder in superconductors with scanning probe microscopy and data analytics

Disorder is a powerful approach to elicit and control superconducting properties, as evidenced from record Tc's, quantum phase transitions and exotic quasiparticles, predicted or evidenced in the presence of disorder. Systematic characterization of disorder fields in superconductors requires generally capturing orders of magnitude in length and temperature scales, posing a potent problem for both data acquistion and analysis. Here we will demonstrate emerging approaches to categorize disorder in notoriously heterogeneous scanning tunneling microscopy (STM) images of unconventional superconductors. From the information centric point of view, understanding the structure of these datasets amounts to effective and physically meaningful data compression. We will discuss compressibility of various kinds of STM data, and demonstrate the follow-on applications of compressive sensing, machine learning and information theory as a way to understand the results of the experiments and improve data acquisition. In particular, similarity learning emerges as a consistent strategy to categorize disorder with minimum prior knowledge. Finally, we apply disorder analysis to differentiate between Josephson and Andreev currents on the atomic scale.