First Principles and Machine Learning Identify Key Pairing Strength Factors of Cuprate Superconductors

Aug 5, 2026

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Band-structure calculations are used to extract and classify density-of-states (DoS) peak features from cuprate superconductors, guided by crystal-structure laws. Orbital interactions involving in-plane and out-of-plane copper-oxygen plane ions are analyzed through peak position, half-width, and height for 35 systems with literature Tc-maximum records. Seven machine-learning algorithms mine the relationship between Tc,max and these orbital parameters, revealing that key pairing-related factors involve not only a flat band but also a newly identified core-orbital interaction deeper in the energy spectrum.

LanguageEnglish

CategoryResearch & Report

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Pages9

Reading Time23 min

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Abstract

Introduction

Method

First Principles and Machine Learning Identify Key Pairing Strength Factors of Cuprate Superconductors Xinyu He1, Ning Chen1, Jingpei Chen1, Xuezhou Wang1*, Yang Li2* 1School of Materials Science and Engineering, 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 *Corresponding author：[nchen@sina.com](nchen@sina.com)； [yang.li@upr.edu](yang.li@upr.edu)[ ](yang.li@upr.edu)Abstract By using band structure calculations of quantum mechanical theory, some important peaks of DoS (Density of States) were obtained and classified based on crystal structure laws of cuprate superconductivity. In particular, the orbital interactions of the in-plane and out-of-plane ions of the copper-oxygen plane were investigated. The position, half-width, and height of DOS peak features were collected for all 35 typical curate systems which have critical temperature maximum data from the works of literature. By training test of 7 common machine learning algorithms, the relationship between the Tc maximum values and these orbital interaction parameters were mined. It was found that the key features of the orbital interaction affecting the Tc maximum were not only the flat band but also a new interaction between core orbitals in a deeper energy band position. Introduction The electron pairing mechanism of high-temperature superconductivity has been oneof the most challenges of condensed matter physics for almost four decays1 as a result of a number of complex and deeply hidden factors influencing on the critical temperature (Tc) of superconductivity, where Tc represents the stiffness of superconductivity which combines with both electronic pairing factors and carrier concentration or doping factors 2. By means of experimental studies on Tc variations with environment, composition and structure of materials, these above two kinds of influence factors had been found3 and some complex relationships were also understood through machine learning (ML) studied on a large data of 12,000 Tc values.4,5 However, the governing strength of pairing factors remains unknown because of the following two technical problems. The first one is that the Tc Raw data’s weights distribute mainly on doping factors but less on pairing ones. For example, nearly 6000 experimental data of Tc values cover mainly 35 of typical systems with only one Tc maximum value for each system, or only 6% data weight of pairing factor, so that the predicted ML model was trained out not a new system with a higher Tc maximum or a stronger pairing factor, but only a new one with suitable doping in fact. 6,7 As the Tc maximum is different in each system fora similar optimal doping of copper oxides 8, the pairing strength of one system should be replaced by its Tc maximum values for ML training test in order to search for pairing factors. On the other hand, the second problem is that these pairing factors were mainly observed from features or attributions of atoms or ions rather than explicit orbitals or electronic interactions9. Although electronic structures could be easily obtained by the first principal approach of quantum physics, it is hard to tackle with both these doped models’ complex constructions and these burden computations for thousands of doping systems. Even if this problem were solved, the limited data set problem still remains due to amuch low weight ratio on the pairing factor. Therefore, changing target data set of the Tc maximum as well as training by key orbital features is the only way to solve the existing technical problems. Method For cuprates, there are three crystal categories: the layer structure for Hg, Tl, Pb and Bi families, the 123 structure and the 214 structure. But even for one structure, there is also a lot of complex orbital interaction features to be considered. Here we should provide a simpler method which is b

FAQs

What DoS peak features are extracted for cuprate superconductors?

Peak position, half-width, and height from density-of-states (DoS) diagrams are collected and classified for the relevant bands.

How is the learning target chosen to focus on pairing factors?

Instead of training on Tc data distributed mainly by doping factors, the model uses Tc maximum values for each system to better represent pairing strength during training.

Which orbital-related factors are found to influence Tc maximum?

Key features include not only the flat band but also a new interaction between core orbitals located deeper in the energy band position.

Aug 5, 2026

Upload by Himbo