Flat bands in full-Heusler crystals – statistical analysis with periodic table deep learning model

Materials with flat bands near or at the Fermi level are a promising route towards strongly correlated states, but the properties demonstration has been severely hindered due to the lack of materials for realization of flat bands. Machine learning is a promising way to speeding up the unearthing of the flat band materials. Here, we propose a convolutional neural network classification model, which only has the periodic table as the input and thus is called periodic table representation (PTR) classifier, to explore flat bands along the high-symmetry paths around the Fermi level and search for the physics behind it. The full-Heusler crystals are chosen as targets because of their abundance in dataset and their much high symmetry with the space group of 225. The PTR model is trained with the full-Heusler crystals in the AFLOW database and then it can accurately classify the flat bands with the AUC of 0.91 for the test set and 0.88 for the full-Heusler crystals in the materials project (MP) dataset. Visualizing the model also gets some interesting phenomina. For example, the model regards the number of valence electrons of the crystal as an important parameter for the flat band prediction: crystals have a high probability to have flat band around the Fermi level if they have valence electrons of about 12×n (n=1,2,3…); crystals have a probability as high as 0.8 to possesse flat bands if their number of unfilled d-orbital electrons is around 6, and the larger number of unfilled p-orbital electrons, the smaller flat band probability. The full-Heusler crystals are reach in magnetic crystals and the PTR can also predict both the flat bands and the ferromagnetic full-Heusler compounds with the accuracy of 0.76. Our work not only provides a quick way to enriching the flat band database, but also provides the specific direction for searing for the flat bands.