Quantitative spin-dependent electron-electron interaction to calculate the superconducting parameters μ and λ

Abstract

The spin-dependent Kukkonen-Overhauser (KO) effective electron-electron interaction in electron gas with a deformable background is used to calculate the BCS superconducting parameters μ, μ*, and λ. The density and spin local field factors are utilized to incorporate the quantitative effects of exchange and correlation. The repulsive parameter μ is compared to results using the historical Thomas-Fermi or nearly equivalent random phase approximation (RPA) interactions. The resulting μ using the KO interaction is 45% larger at rs=1.65; rising to 153% larger at rs=5.62. Retardation reduces the effective repulsion, but μ* is still 20−25% larger. The predicted superconducting transition temperature would be reduced by 5−20% using the McMillan formula. The attractive superconducting parameter λ, which depends on the electron-test charge interaction and the phonon spectrum, is also calculated using simple Debye-based models for phonon dispersion. This leads to a larger value of λ than the same calculation using Thomas-Fermi or RPA interactions. Modern calculations of the phonon dispersion relations are often done using density functional theory. With the proper exchange and correlation kernel, the self-consistency of the method should yield the correct phonon dispersion relation and electron-phonon matrix elements. If the Thomas-Fermi or RPA interactions are used at any stage, the results for λ are probably quantitatively inaccurate.

Similar papers