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Acta Physica Sinica

THE CORRELATION FUNCTION OF TWO DIMENSIONAL ELECTRON GAS

X Xiong

Published Jan 1, 1989• 0 citations
OpenAlex

Abstract

The correlation function of two dimensional electron gas with the presence of a strong perpendicular magnetic field has been studied on the basis of the wave function in small system. A formula of the correlation function of a finite cluster has been obtained for numerical calculation.

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THE CORRELATION FUNCTION OF TWO DIMENSIONAL ELECTRON GAS

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Green’s function of a two-dimensional interacting electron gas in a perpendicular magnetic field

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We study the two-dimensional electron gas in a quantizing magnetic field for the cases of Coulomb and harmonic interactions among the electrons. Numerical solutions for the quantum states of clusters of up to five electrons show that the strength of the excitation gap is a strongly oscillating function of the density not unlike what is observed in the anomalous quantum Hall effect. We present analytic results for the case of harmonic interactions and show that the variational wave function recently proposed by Laughlin for the Coulomb problem is in fact an exact eigenstate of the harmonic problem.
The ground state of an electron gas in an intense magnetic field is studied using a wave function of the product form ${\ensuremath{\Psi}}_{0}^{B}\ensuremath{\Phi}$. The correlation factor ${\ensuremath{\Psi}}_{0}^{B}$ is taken to be the ground-state solution of a charged Bose gas and $\ensuremath{\Phi}$ a determinant of single-particle Landau states. In the quantum strong-field limit so that only the lowest Landau state is populated, the correlation energy is computed using the cluster-expansion technique and a variational determination of the boson energy. Numerical results obtained are lower than those derived under the random-phase approximation.