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 function- als 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.

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

PROFETA, Gianni;CONTINENZA, Alessandra;
2005-01-01

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 function- als 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.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11697/18669
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