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Electron liquid

About: Electron liquid is a research topic. Over the lifetime, 767 publications have been published within this topic receiving 39908 citations.


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TL;DR: The authors assess various approximate forms for the correlation energy per particle of the spin-polarized homogeneous electron gas that have frequently been used in applications of the local spin density a...
Abstract: We assess various approximate forms for the correlation energy per particle of the spin-polarized homogeneous electron gas that have frequently been used in applications of the local spin density a...

17,531 citations

Journal ArticleDOI
TL;DR: The spin-density-functional (SDF) formalism has been used for the interpretation of approximate versions of the theory, in particular the local-spin-density (LSD) approximation, which is formally valid only in the limit of slow and weak spatial variation in the density as discussed by the authors.
Abstract: The aim of this paper is to advocate the usefulness of the spin-density-functional (SDF) formalism. The generalization of the Hohenberg-Kohn-Sham scheme to and SDF formalism is presented in its thermodynamic version. The ground-state formalism is extended to more general Hamiltonians and to the lowest excited state of each symmetry. A relation between the exchange-correlation functional and the pair correlation function is derived. It is used for the interpretation of approximate versions of the theory, in particular the local-spin-density (LSD) approximation, which is formally valid only in the limit of slow and weak spatial variation in the density. It is shown, however, to give good account for the exchange-correlation energy also in rather inhomogeneous situations, because only the spherical average of the exchange-correlation hole influences this energy, and because it fulfills the sum rule stating that this hole should contain only one charge unit. A further advantage of the LSD approximation is that it can be systematically improved. Calculations on the homogeneous spin-polarized electron liquid are reported on. These calculations provide data in the form of interpolation formulas for the exchange-correlation energy and potentials, to be used in the LSD approximation. The ground-state properties are obtained from the Galitskii-Migdal formula, which relates the total energy to the one-electron spectrum, obtained with a dynamical self-energy. The self-energy is calculated in an electron-plasmon model where the electron is assumed to couple to one single mode. The potential for excited states is obtained by identifying the quasiparticle peak in the spectrum. Correlation is found to significantly weaken the spin dependence of the potentials, compared with the result in the Hartree-Fock approximation. Charge and spin response functions are calculated in the long-wavelength limit. Correlation is found to be very important for properties which involve a change in the spinpolarization. For atoms, molecules, and solids the usefulness of the SDF formalism is discussed. In order to explore the range of applicability, a few applications of the LSD approximation are made on systems for which accurate solutions exist. The calculated ionization potentials, affinities, and excitation energies for atoms propose that the valence electrons are fairly well described, a typical error in the ionization energy being 1/2 eV. The exchange-correlation holes of two-electron ions are discussed. An application to the hydrogen molecule, using a minimum basis set, shows that the LSD approximation gives good results for the energy curve for all separations studied, in contrast to the spin-independent local approximation. In particular, the error in the binding energy is only 0.1 eV, and bond breaking is properly described. For solids, the SDF formalism provides a framework for band models of magnetism. An estimate of the splitting between spin-up and spin-down energy bands of a ferromagnetic transition metal shows that the LSD approximation gives a correction of the correct sign and order of magnitude to published $X\ensuremath{\alpha}$ results. To stimulate further use of the SDF formalism in the LSD approximation, the paper is self-contained and describes the necessary formulas and input data for the potentials.

2,763 citations

Journal ArticleDOI
TL;DR: In this paper, the two-fluid model is used to describe the behavior of a superfluid in response to a transverse probe in a two-fluid model.
Abstract: Special Preface -- Preface -- Special Preface -- Preface -- Introduction -- Neutral Fermi Liquids -- Response and Correlation in Neutral Systems -- Charged Fermi Liquids -- Response and Correlation in Homogeneous Electron Systems -- Microscopic Theories of the Electron Liquid -- Introduction -- Experimental And Theoretical Background On He II -- Elementary Excitations -- Elementary Excitations in He II -- Superfluid Behavior: Response To A Transverse Probe. Qualitative Behavior Of A Superfluid -- Superfluid Flow: Macroscopic Limit -- Basis for the Two-Fluid Model -- First, Second, And Quasi-Particle Sound -- Vortex Lines -- Microscopic Theory: Uniform Condensate -- Microscopic Theory: Non-Uniform Condensate -- Conclusion -- * Second Quantization

2,494 citations

Journal ArticleDOI
TL;DR: It is argued that zero-energy Majorana bound states are formed in various situations when such wires are situated in proximity to a conventional s-wave superconductor when the external magnetic field, the superconducting gap, or the chemical potential vary along the wire.
Abstract: We show that the combination of spin-orbit coupling with a Zeeman field or strong interactions may lead to the formation of a helical electron liquid in single-channel quantum wires, with spin and velocity perfectly correlated. We argue that zero-energy Majorana bound states are formed in various situations when such wires are situated in proximity to a conventional s-wave superconductor. This occurs when the external magnetic field, the superconducting gap, or, most simply, the chemical potential vary along the wire. These Majorana states do not require the presence of a vortex in the system. Experimental consequences of the helical liquid and the Majorana states are also discussed.

2,470 citations

Book
01 Apr 2005
TL;DR: In this paper, the Hartree-Fock approximation is used to approximate the linear response of an interacting electron liquid and the perturbative calculation of linear response functions is performed. But the results are limited to the one-dimensional electron gas at high magnetic field.
Abstract: 1. Introduction to the electron liquid 2. The Hartree-Fock approximation 3. Linear response theory 4. Linear response of independent electrons 5. Linear response of an interacting electron liquid 6. The perturbative calculation of linear response functions 7. Density functional theory 8. The normal Fermi liquid 9. The one-dimensional electron gas and the Luttinger liquid 10. The two-dimensional electron gas at high magnetic field.

1,084 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202120
202022
201914
201814
201718
201625