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Ab-initio theory of superconductivity -- I: Density functional formalism and approximate functionals
Authors: M. Lüders, M.A.L. Marques, N.N. Lathiotakis, A. Floris, G. Profeta, L. Fast, A. Continenza, S. Massidda, and E.K.U. Gross
Ref.: Phys. Rev. B 72, 024545 (2005)
Abstract: A novel 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 Schroedinger 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.
Citations: 207 (Google scholar)
DOI: 10.1103/PhysRevB.72.024545
URL: arxiv.org
Bibtex:
@article{L_ders_2005,
doi = {10.1103/physrevb.72.024545},
url = {https://doi.org/10.1103%2Fphysrevb.72.024545},
year = 2005,
month = {jul},
publisher = {American Physical Society ({APS})},
volume = {72},
number = {2},
author = {M. Lüders and M. A. L. Marques and N. N. Lathiotakis and A. Floris and G. Profeta and L. Fast and A. Continenza and S. Massidda and E. K. U. Gross},
title = {$\less$i$\greater$Ab initio$\less$/i$\greater$theory of superconductivity. I. Density functional formalism and approximate functionals},
journal = {Physical Review B}
}