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Bulletin of the American Physical Society

Absence of certain exchange driven instabilities of an electron gas at high densities

Gabriele F. Giuliani, Giovanni Vignale

Published Mar 6, 2007• 0 citations
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Abstract

In the high-density limit the exchange energy easily overcomes the correlation energy in both two- and three-dimensional electron liquids. It is therefore reasonable to inquire if the class of exchange driven instabilities first discussed by Overhauser within the Hartree-Fock theory could be of relevance in this limit. Our analysis shows that this is not the case at least for distorted states represented by a single Slater determinant.

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In the high-density limit the exchange energy easily overcomes the correlation energy in both two- and three-dimensional electron liquids. It is therefore reasonable to inquire if the class of exchange driven instabilities first discussed by Overhauser within the Hartree-Fock theory could be of relevance in this limit. Our analysis shows that this is not the case at least for distorted states represented by a single Slater determinant.
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 LixZrNCl{\mathrm{Li}}_{x}\mathrm{Zr}\mathrm{N}\mathrm{Cl}Lix​ZrNCl superconductors.
Two infinite families of two-parameter generalized Overhauser orbitals are introduced and shown to satisfy explicitly, for occupied states, the self-consistent Hartree-Fock equations in the thermodynamic limit. For an attractive $\ensuremath{\delta}$ interaction, they give lower Hartree-Fock energy than the usual plane-wave solutions, even for relatively weak coupling and/or low density. The limiting members (possessing an infinite number of harmonics) of both families appear to tend to a "classical static lattice" state, via a second-order transition for one family and via first order for the other. The related density profiles and energy expressions are calculated as functions of the two new parameters. A direct variation with respect to these parameters was done numerically and results are presented graphically.
The spin-density wave (SDW) state of the uniform electron gas is investigated in the exact-exchange approximation of noncollinear spin-density functional theory (DFT). Unlike in Hartree-Fock theory, where the uniform paramagnetic state of the electron gas is unstable against formation of the spin-density wave for all densities, in exact-exchange spin DFT this instability occurs only for densities lower than a critical value. It is also shown that, although in a suitable density range it is possible to find a noninteracting SDW ground-state Slater determinant with energy lower than the corresponding paramagnetic state, this Slater determinant is not a self-consistent solution of the optimized effective potential (OEP) integral equations of noncollinear spin DFT. A self-consistent solution of the OEP equations which gives an even lower energy can be found using an excited-state Slater determinant where only orbitals with single-particle energies in the lower of two bands are occupied while orbitals in the second band remain unoccupied even if their energies are below the Fermi energy.