Ab initio theory of superconductivity. I. Density functional formalism and approximate functionals

M. Lüders*, M. A.L. Marques, N. N. Lathiotakis, A. Floris, G. Profeta, L. Fast, A. Continenza, S. Massidda, E. K.U. Gross

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

239 Scopus citations


An approach to the description of superconductors in thermal equilibrium is developed within a formally exact density functional framework. The theory is formulated in terms of three "densities:" the ordinary electron density, the superconducting order parameter, and the diagonal of the nuclear N -body density matrix. The electron density and the order parameter are determined by Kohn-Sham equations that resemble the Bogoliubov-de Gennes equations. The nuclear density matrix follows from a Schrödinger equation with an effective N -body interaction. These equations are coupled to each other via exchange-correlation potentials which are universal functionals of the three densities. Approximations of these exchange-correlation functionals are derived using the diagrammatic techniques of many-body perturbation theory. The bare Coulomb repulsion between the electrons and the electron-phonon interaction enter this perturbative treatment on the same footing. In this way, a truly ab initio description is achieved which does not contain any empirical parameters.

Original languageAmerican English
Article number024545
JournalPhysical Review B - Condensed Matter and Materials Physics
Issue number2
StatePublished - 1 Jul 2005
Externally publishedYes


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