Extracting causality from spectroscopy.

Causality represents a directed relationship where one state, designated as a cause, directly produces or partially influences another state, an effect. Identifying causality in observations of physical phenomena is a core challenge in science, as it reveals the fundamental laws governing these observations. However, extracting causal relationships from complex data remains difficult. While recent advances in machine learning offer promising avenues, a definitive guiding principle for its application for causal inference has yet to emerge. Here, we propose a protocol to analyze spectroscopy data using DirectLiNGAM, one of statistical causal inferences for learning a Linear Non-Gaussian Acyclic Model. We applied this approach to spatially resolved core-level photoemission spectroscopy measurements of the kagome superconductor CsV₃Sb₅. Our analysis uncovered intriguing causal relationships among Cs surface coverage, core-level intensity/position, and the spectral background. These findings provide an explanation for the polar surface formation in CsV₃Sb₅ and, furthermore, reveal an unexpected causal link in the intensity of spin-orbit satellite peaks. These results highlight the potential of our method to reveal new physical laws that would be difficult to identify using conventional data analysis techniques.