Machine learning the relationship between Debye temperature and superconducting transition temperature

Abstract

Recently a relationship between the Debye temperature ΘD and the superconducting transition temperature Tc of conventional superconductors has been proposed [Esterlis et al., npj Quantum Mater. 3, 59 (2018)]. The relationship indicates that Tc≤AΘD for phonon-mediated BCS superconductors, with A being a prefactor of order ∼0.1. In order to verify this bound, we train machine learning (ML) models with 10 330 samples in the Materials Project database to predict ΘD. By applying our ML models to 9860 known superconductors in the NIMS SuperCon database, we find that the conventional superconductors in the database indeed follow the proposed bound. We also perform first-principles phonon calculations for H3S and LaH10 at 200 GPa. The calculation results indicate that these high-pressure hydrides essentially saturate the bound of Tc versus ΘD.