Information Extraction from Fermi Surfaces Using Unsupervised Machine Learning

Fermi surface is crucial information for the designing various functions in spintronics devices. Particularly, electron states such as Weyl point and nodal line on Fermi surface contribute to spin polarization and anomalous Nernstian effects. However, a great deal of expertise and effort is required to analyze Fermi surfaces and discuss their mechanisms. Moreover, the volume of Fermi surface data has been rapidly increasing due to recent advancements in high-throughput angle-resolved photoelectron spectroscopy（ARPES）measurements at next-generation synchrotrons. Accordingly, there is a significant demand for extracting information on physical properties through the automated analysis of Fermi surfaces. In this study, we applied machine learning to the Fermi surface of Heusler alloy Co₂MnGa_xGe_1-x (CMGG) and visualized the regions contributing to physical properties.<br/>The band structures of CMGG were calculated with 1 at% increments using the first-principles calculation program VASP. The Fermi surface was prepared on the k_x-k_y plane from the calculated band structures, similar to ARPES data. Spin polarization at the Fermi level for each composition was calculated from the density of states (DOS). We performed dimensionality reduction using principal component analysis (PCA), which has high explanatory power and enables anomaly detection, to visualize data changes and extract features in high-dimensional datasets.<br/>Composition-dependent Fermi surface changes were visualized in two-dimensional space using PCA. The distances between data points correspond to changes in the Fermi surface. We could confirm significant “jumps” in certain compositions in the reduced two-dimensional space. The data jumps at Ga=15, 24, and 38 at% corresponded to the compositions where there were local maximum or local minimum in the spin polarization changes. Additionally, the jump around Ga=77-79 at% corresponded to a composition where the majority band changed significantly, greatly affecting the spin polarization. By dimensional reduction of the Fermi surface data, we were able to automatically extract compositions related to the spin polarization. Furthermore, for compositions around Ga=94-95%, not only were data jumps observed, but there were also regions that deviated from the data trend. Detailed analysis of the band structure revealed that these compositions had gapped Weyl points at the Fermi level. These results demonstrate the success of using unsupervised machine learning to reduce the dimensionality of the complex Fermi surface and visualize it in data space, allowing for the automatic extraction of noteworthy compositions and features. To verify the robustness of this analysis method against noise data, we tested it by adding noise. Although the contribution rate of dimensionality reduction decreased with increased Gaussian and Poisson noise, the shape in data space was preserved to some extent. By performing the previously analysis, we were still able to automatically extract noteworthy compositions and features despite the noise.<br/>In this study, we applied unsupervised machine learning to the Fermi surface of CMGG, successfully constructing a relationship between changes in the Fermi surface shape and spin polarization in data space. This enabled us to automatically visualize features that explain the spin polarization and identify notable regions on the Fermi surface. Additionally, we successfully extracted compositions where special electronic states, such as Weyl points, appear on Fermi level. We expected that this developed automated analysis method can be applied to actual ARPES measurement data to extract buried information in band structures and handle data with high noise levels.