Prediction of Tc Upper Limits for Superconducting Materials Assisted by Machine Learning

Haiyou Huang¹*, Yang Liu¹, Yan Zhang¹, Hongyuan Feng¹, Ning Chen¹, Yang Li², Kui Jin³, Dezhen Xue⁴, Yanjing Su¹

¹ University of Science and Technology Beijing, Beijing, 100083, China.

² Department of Engineering Science and Materials, University of Puerto Rico, Mayaguez, Puerto Rico 00681-9000, USA.

³ Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China.

⁴ State Key Laboratory for Mechanical Behavior of Materials, Xi'an Jiaotong University, Xi'an 710049, China.

ABSTRACT: Finding room temperature superconductors is a dream of generations. However, in reality, finding a superconductor is easy, finding a high temperature superconductor is hard. We are so longing for a convenient way to predict the critical temperature (T_c) of the superconductors. Owing that there are multiple factors affecting the superconductivity, we need a holistic perspective to learn the variation law of T_c. So, the problem of the superconductivity is to find the pattern in high dimensional space of the factors affecting T_c, is exactly calling for the help of the machine learning (ML). Usually, when taking about predict superconductors, we are thinking of two goals: one is to foresee a material superconduct or not, the other is to predict the T_c of each chemical composition.

However, for the ML, those two goals are less feasible. It is hard to know whether a material superconduct or not before knowing its magnetism, which is also unpredictable for now. On the other hand, the need of materials scientists is to predict brand new materials, instead of composition optimization. There is no need to predict the T_c of each composition, the ML should be used to predict the T_c maxima (T_c^max) of various kinds of materials. Hence, owing that our goal is to predict the T_c^max of new materials, the generalization ability of the ML models is of great significance.

Recently, encouraging progresses have been made in several ML studies on the T_c of superconductors. So far, the predictive score on the test data is quite good. However, their performance of those ML models on predicting unknown materials is not examined. We noticed that the previous studies, the T_c and the T_c^max were often confused with each other. The models were trained with the data of T_c, but prediction is on the T_c^max. Actually, they are two properties having very different meanings. Owing that the data distribution of the T_c is obviously imbalanced, the models trained with the T_c have poor generalization ability, which makes it not suitable for the prediction of the T_c^max. When predicting the T_c^max, the generalization ability of the models is the key to obtain reliable results.

In this work, we were looking for a strategy to get reliable ML models predicting the T_c^max of superconducting materials. We categorized the data in the superconductor database, obtaining ~1000 kinds of superconducting materials. In each kind of superconducting materials, we choose the highest T_c as the T_c^max of this kind of superconducting materials. Meanwhile, we designed a novel feature set, according to the orbital attributes of the valence electrons. These features may carry the information about the origin of the superconductivity, which lead to better interpretability of the ML models. The ML models trained with the dataset of the T_c^max, and the features derived from the valence electrons, yield good results, which help us find a new universal empirical law of T_c^max. It infers a necessary but insufficient condition of the existence of high T_c^max, providing an effective guidance for the designation of superior superconductors.

Keywords: superconductor；critical temperature；machine learning