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Machine learning the relationship between Debye temperature and superconducting transition temperature
Adam D. Smith, Sumner B. Harris, Renato P. Camata, Da Yan, Cheng-Chien Chen
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Recently a relationship between the Debye temperature Θ_D and the superconducting transition temperature T_c of conventional superconductors has been proposed [npj Quantum Materials 3, 59 (2018)]. The relationship indicates that T_c ≤A Θ_D for phonon-mediated BCS superconductors, with A being a pre-factor 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. By applying our ML models to 9,860 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 T_c versus Θ_D.
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