Relating Debye and Superconducting Transition Temperatures by Machine Learning in Conventional Superconductors

Recently a relationship between the Debye temperature $\Theta_D$ and the superconducting transition temperature $T_c$ of conventional superconductors has been proposed [in npj Quantum Materials $\mathbf{3}$, 59 (2018)]. The relationship indicates that for phonon-mediated BCS superconductors the maximum $T_c$ is at most $\sim 0.1\times \Theta_D$. In order to verify this bound and develop tools for predicting the Debye temperature, we trained Machine Learning models on over 10000 compounds with just chemical formula and crystal system information as features. By examining 5000 known superconducting compounds in the NIMS SuperCon database, our predictions show that the conventional superconductors in the database indeed follow the previously proposed bound of $T_c$ vs. $\Theta_D$. We also discuss our manual selection criteria and Machine Learning clustering techniques to separate conventional superconductors from others in the NIMS SuperCon database.