## Abstract

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 language | American English |
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Article number | 024545 |

Journal | Physical Review B - Condensed Matter and Materials Physics |

Volume | 72 |

Issue number | 2 |

DOIs | |

State | Published - 1 Jul 2005 |

Externally published | Yes |