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Benchmark of density functional theory for superconductors in elemental materials

Systematic benchmark calculations for elemental bulks are presented to validate the accuracy of density functional theory for superconductors. We developed a method to treat the spin-orbit interaction (SOI) together with the spin fluctuation (SF) and examine their effect on the superconducting transition temperature. We found the following results from the benchmark calculations: (1) The calculations, including SOI and SF, reproduce the experimental superconducting transition temperature ($T_c$) quantitatively. (2) The effect by SOI is small excepting a few elements such as Pb, Tl, and Re. (3) SF reduces $T_c$s, especially for the transition metals, while this reduction is too weak to reproduce the $T_c$s of Zn and Cd. (4) We reproduced the absence of superconductivity for alkaline (earth) and noble metals. These calculations confirm that our method can be applied to a wide range of materials and implies a direction for the further improvement of the methodology.