Ab initio study on the high superconducting transition temperature in calcium under high pressure†

Abstract

For calcium in the phases IV and V, we estimated the superconducting transition temperature T c by the use of the Allen–Dynes formula. Setting the effective screened Coulomb repulsion constant μ* at 0.1 in the formula, we obtained T c =23.42 K at 100 GPa for Ca-IV and T c =15.87 K at 120 GPa for Ca-V. In order to clarify the origin of such high values of T c , first, we investigated the band character of electrons and found that the high T c is not necessarily related to the so called s–d transfer. Then we analyzed the electron–phonon coupling at each phonon mode in Ca-V where the highest T c in elements has been experimentally observed. As a result, we discovered that an optical mode at the Γ point has the strongest electron–phonon coupling. Such phonon mode can exist only in the complex crystal structure of Ca-V, and the result shows that the high T c seems to be closely linked with the complex crystal structures like Ca-IV and Ca-V. †This paper was presented at the XLVIth European High Pressure Research Group (EHPRG 46) Meeting, Valencia (Spain), 7–12 September, 2008.