Machine learning the relationship between Debye temperature and superconducting transition temperature
Recently a relationship between the Debye temperature $Θ_D$ and the superconducting transition temperature $T_c$ of conventional superconductors has been proposed [Esterlis et al., npj Quantum Mater. 3, 59 (2018)]. The relationship indicates that $T_c$ ≤ $AΘ_D$ 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 $Θ_D$. Here, 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 $\mathrm{H_3S}$ and $\mathrm{LaH_{10}}$ at 200 GPa. The calculation results indicate that these high-pressure hydrides essentially saturate the bound of $T_c$ versus $Θ_D$.