Machine Learning the Relationship Between Debye and Superconducting Transition Temperatures

Recently a relationship between the Debye temperature Θ_D and the superconducting transition temperature T_c of conventional superconductors has been proposed [in npj Quantum Materials 3, 59 (2018)]. The relationship indicates that for phonon-mediated BCS superconductors, the maximum possible T_c is ~ 0.1Θ_D. In order to verify this bound, we train machine learning (ML) models on over 10,000 compounds to predict the Debye temperature, using only chemical formula and crystal system information as input features. By examining 5,000 known superconducting compounds in the NIMS SuperCon database, we show that conventional superconductors in the database indeed follow the previously proposed bound of T_c versus Θ_D. We also present our manual selection criteria and ML classification techniques to separate conventional superconductors from others in the database. Some insights on how T_c could be boosted closer to the bound will be discussed.