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Concept
Jellium
Summary
Jellium, also known as the uniform electron gas (UEG) or homogeneous electron gas (HEG), is a quantum mechanical model of interacting electrons in a solid where the positive charges (i.e. atomic nuclei) are assumed to be uniformly distributed in space; the electron density is a uniform quantity as well in space. This model allows one to focus on the effects in solids that occur due to the quantum nature of electrons and their mutual repulsive interactions (due to like charge) without explicit introduction of the atomic lattice and structure making up a real material. Jellium is often used in solid-state physics as a simple model of delocalized electrons in a metal, where it can qualitatively reproduce features of real metals such as screening, plasmons, Wigner crystallization and Friedel oscillations.
At zero temperature, the properties of jellium depend solely upon the constant electronic density. This property lends it to a treatment within density functional theory; the formalism itself provides the basis for the local-density approximation to the exchange-correlation energy density functional.
The term jellium was coined by Conyers Herring in 1952, alluding to the "positive jelly" background, and the typical metallic behavior it displays.
The jellium model treats the electron-electron coupling rigorously. The artificial and structureless background charge interacts electrostatically with itself and the electrons. The jellium Hamiltonian for N electrons confined within a volume of space Ω, and with electronic density ρ(r) and (constant) background charge density n(R) = N/Ω is
where
Hel is the electronic Hamiltonian consisting of the kinetic and electron-electron repulsion terms:
Hback is the Hamiltonian of the positive background charge interacting electrostatically with itself:
Hel-back is the electron-background interaction Hamiltonian, again an electrostatic interaction:
Hback is a constant and, in the limit of an infinite volume, divergent along with Hel-back.
Official source
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