A universal LDA-type density functional describing the electronic correlations in superconductors is developed from first principles. The functional is constructed from the exchange-correlation free-energy density, ${f}_{\mathrm{xc}}^{\mathrm{hom}}$ , of a homogeneous electron gas exposed to an external translationally invariant pairing field. The quantity ${f}_{\mathrm{xc}}^{\mathrm{hom}}$ , which is a function of the density and a functional of the induced order parameter, is calculated by many-body perturbation theory.A universal LDA-type density functional describing the electronic correlations in superconductors is developed from first principles. The functional is constructed from the exchange-correlation free-energy density, ${f}_{\mathrm{xc}}^{\mathrm{hom}}$, of a homogeneous electron gas exposed to an external translationally invariant pairing field. The quantity ${f}_{\mathrm{xc}}^{\mathrm{hom}}$, which is a function of the density and a functional of the induced order parameter, is calculated by many-body perturbation theory.

Physical Review LettersSep 27, 199947 citations

Electron-electron interaction in a two-dimensional electron gas: Bound states at low densities

I. Nagy, Martti J. Puska, Nerea Zabala

If the bare interaction between two electrons is dressed in the two-dimensional electron gas by the response of the many-body environment, pairing may occur. Here, we study numerically the existence and character of bound states in the case where the dressing in the pair-interaction energy is described by the Overhauser geminal model [A. W. Overhauser, Can. J. Phys. 75, 683 (1995)]. The starting point of the model is the exchange correlation hole around a single electron. We constrain the hole by arguments based on the results for the exchange-correlation energy and the contact density of the pair-correlation function. We find a bound state with the energy minimized at a certain electron gas density. On the basis of the behavior of the binding energy we discuss recent experimental findings for the electron density dependence of the critical temperature in cuprate, Chevrel-phase, and Li-intercalated ${\mathrm{Li}}_{x}\mathrm{Zr}\mathrm{N}\mathrm{Cl}$ superconductors.If the bare interaction between two electrons is dressed in the two-dimensional electron gas by the response of the many-body environment, pairing may occur. Here, we study numerically the existence and character of bound states in the case where the dressing in the pair-interaction energy is described by the Overhauser geminal model [A. W. Overhauser, Can. J. Phys. 75, 683 (1995)]. The starting point of the model is the exchange correlation hole around a single electron. We constrain the hole by arguments based on the results for the exchange-correlation energy and the contact density of the pair-correlation function. We find a bound state with the energy minimized at a certain electron gas density. On the basis of the behavior of the binding energy we discuss recent experimental findings for the electron density dependence of the critical temperature in cuprate, Chevrel-phase, and Li-intercalated ${\mathrm{Li}}_{x}\mathrm{Zr}\mathrm{N}\mathrm{Cl}$ superconductors.

Physical Review BJun 29, 20072 citations

Electron Correlations in Strongly Interacting Systems

J. J. Quinn, George Simion

WORLD SCIENTIFIC eBooksMay 1, 20101 citation

Short-ranged correlations and the ferromagnetic electron gas

A. K. Rajagopal, John C. Kimball, Mahadev Banerjee

A discussion of the various properties of pair correlation functions of a magnetic electron gas is presented. The cusp conditions obeyed by the many-electron wave functions for a pair of electrons with parallel and antiparallel spins in close proximity are expressed as derivative conditions on the corresponding parallel-and antiparallel-spin pair correlation functions. In particular, it is shown that in a fully ferromagnetic gas the parallel spin correlations determine the correlation energy whereas in the paramagnetic case, this function is of less importance in comparison to the antiparallel-spin correlation function. In the high-momentum limit, it is found that the momentum distribution of electrons is dominated by antiparallel-spin correlations in the partially magnetic case whereas in the fully ferromagnetic case, it is dominated by parallel-spin correlations but is smaller by a factor of ${q}^{\ensuremath{-}2}$. A calculation of the parallel-spin correlation function for the ferromagnetic gas in perturbation theory is presented. A model for the exchange correlation energy of the system which takes into account the exact conditions given here is proposed. Corresponding results for the two-dimensional electron gas are also stated.A discussion of the various properties of pair correlation functions of a magnetic electron gas is presented. The cusp conditions obeyed by the many-electron wave functions for a pair of electrons with parallel and antiparallel spins in close proximity are expressed as derivative conditions on the corresponding parallel-and antiparallel-spin pair correlation functions. In particular, it is shown that in a fully ferromagnetic gas the parallel spin correlations determine the correlation energy whereas in the paramagnetic case, this function is of less importance in comparison to the antiparallel-spin correlation function. In the high-momentum limit, it is found that the momentum distribution of electrons is dominated by antiparallel-spin correlations in the partially magnetic case whereas in the fully ferromagnetic case, it is dominated by parallel-spin correlations but is smaller by a factor of ${q}^{\ensuremath{-}2}$. A calculation of the parallel-spin correlation function for the ferromagnetic gas in perturbation theory is presented. A model for the exchange correlation energy of the system which takes into account the exact conditions given here is proposed. Corresponding results for the two-dimensional electron gas are also stated.

Physical review. B, Condensed matterSep 1, 1978117 citations

{f}_{\mathrm{xc}}^{\mathrm{hom}}

, of a homogeneous electron gas exposed to an external translationally invariant pairing field. The quantity

{f}_{\mathrm{xc}}^{\mathrm{hom}}

, which is a function of the density and a functional of the induced order parameter, is calculated by many-body perturbation theory.

{\mathrm{Li}}_{x}\mathrm{Zr}\mathrm{N}\mathrm{Cl}

superconductors.