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Abstract
We study the properties of a finite two-dimensional electron gas system in the Hartree-Fock approximation. We obtain exact analytical expressions for the energy in a finite two-dimensional fully spin-polarized (spinless) system of electrons interacting with a Coulomb potential immersed in a finite square region uniformly filled with a neutralizing positive charge. The difficult two-electron integrals over the finite square domain are reduced to simple compact expressions involving analytic auxiliary functions. We provide results for the potential energy of systems with a finite number of electrons and show how the energy slowly converges towards its thermodynamic limit bulk value.
Highlights
The jellium model in condensed matter physics is a very common model for treating systems of interacting electrons
We study the properties of a finite two-dimensional electron gas system in the HartreeFock approximation
We obtain exact analytical expressions for the energy in a finite two-dimensional fully spin-polarized system of electrons interacting with a Coulomb potential immersed in a finite square region uniformly filled with a neutralizing positive charge
Summary
The jellium model in condensed matter physics is a very common model for treating systems of interacting electrons. A variety of numerical calculations, mostly based on quantum Monte Carlo methods, have fairly well established the thermodynamic properties of a 3DEG and 2DEG for a wide range of densities.[1,2,3,4,5,6] The most straighforward theoretical treatment of such systems involves use of an anti-symmetrized Slater determinant wave function of plane waves[7] as starting point. Such an approach constitutes the underlying idea of the Hartree-Fock (HF) approximation
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