The search for next-generation electronic materials often starts with studying the Fermi surface, which serves as a map of a material’s electronic structure. Its shape varies with crystal structure, composition, and electronic band arrangement, directly impacting properties such as carrier density, magnetic behavior, and spin polarization. This makes it a crucial tool for understanding and engineering new materials.

AI-Assisted Mapping of Fermi Surface Topology and Nodal Features: conceptual illustration of an interpretable machine learning framework for analyzing complex Fermi surfaces in Heusler alloys. The central patterned surface represents the Fermi surface landscape, where contour variations correspond to electronic structure features. Polyhedral structures depict different compositional states, while colored internal patterns indicate variations in spin polarization. Red markers highlight detected anomalies and key transition points, including extrema and inflection regions. A robotic probe symbolizes experimental input (e.g., angle-resolved photoemission spectroscopy-like data), while the digital hand represents artificial intelligence (AI)-driven analysis using principal component analysis to identify significant “jumps” in feature space. The highlighted central structure illustrates the emergence and localization of nodal lines, automatically detected through outlier-based differential analysis. The overall scene emphasizes robust, noise-tolerant data interpretation and high-throughput discovery of electronic phenomena. Image credit: Professor Masato Kotsugi from Tokyo University of Science, Japan

The Fermi surface of a material is determined experimentally using techniques such as angle-resolved photoemission spectroscopy (ARPES). However, interpreting ARPES data requires specialized expertise, and the measurements themselves are often susceptible to noise. As experiments produce larger amounts of data, carefully reviewing every image by hand becomes time-consuming and inefficient.

To address this challenge, a team from Tokyo University of Science (TUS), Nagoya University, and Kyoto Institute of Technology in Japan developed a machine learning approach to analyze Fermi surface images of a material called Co2MnGaxGe1-x. This material belongs to a family known as Heusler alloys and is of particular interest for spintronics, a field that uses the spin of electrons—rather than only their charge—to process information. The alloy is also known for exhibiting the anomalous Nernst effect, in which a voltage is generated from a temperature difference in a magnetic material. Both phenomena are closely related to special features called nodal lines that appear on the material’s Fermi surface.

The team at TUS included Professor Masato Kotsugi, former Master’s student Daichi Ishikawa, and Kentaro Fuku. “The study contributes to a growing movement that harnesses artificial intelligence (AI) to reveal patterns in materials that might otherwise remain hidden,” says Prof. Kotsugi. The study will be published in the journal Scientific Reports.

The researchers used a technique called principal component analysis (PCA). PCA is a type of unsupervised machine learning that simplifies complex data while keeping the most important patterns. Even though Fermi surfaces can have detailed and complicated shapes, the range of compositions studied in this alloy is relatively narrow, making PCA well-suited for identifying systematic trends.

The researchers began with computer simulations based on density functional theory to calculate the electronic structure of the material at different compositions. From these calculations, the team generated images of the Fermi surface. They also calculated spin polarization, a key property that describes the imbalance between electrons with different spin directions. The Fermi surface images were converted into one-dimensional vectors and analyzed using PCA to identify similarities and differences among compositions.

The method successfully identified the exact compositions where significant changes in the Fermi surface topology occur. In particular, near a gallium concentration of about 0.94 to 0.95, sudden “jumps” in the simplified PCA representation corresponded to the emergence of nodal lines and extrema and inflection points in spin polarization.

Importantly, the method remained effective even when the images were intentionally blurred or strong noise was added to simulate real experimental conditions, mimicking ARPES data, and the approach continued to successfully identify compositions associated with variations in spin polarization and nodal lines.

The findings show that this machine learning approach can quickly highlight important changes in a material’s Fermi surface. Such tools could help scientists screen large datasets more efficiently and accelerate the development of materials with desirable electronic properties. Moreover, its ability to detect outliers through differential analysis in PCA space could be extended to screen other material candidates, including strongly correlated materials with flat bands and Weyl or Dirac semimetals with multiple nodal features, enabling researchers to identify promising material candidates for diverse applications.

Source: Tokyo University of Science