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Physical Review Letters

Exchange Effects in an Artificial Atom at High Magnetic Fields

O. Klein, Claudio Chamon, David Tang David Tang, David Abusch-Magder, U. Meirav, Xiao-Gang Wen, M. A. Kastner, Shalom J. Wind

Published Jan 30, 1995• 106 citations
Publisher

Abstract

A droplet of $N\ensuremath{\sim}30$ electrons is created by lateral confinement of a two-dimensional electron gas. The evolution of its chemical potential ${\ensuremath{\mu}}_{N}$ with magnetic field $B$ is inferred from resonant tunneling experiments and is used to study the dependence of its magnetization on $B$.The experimental data, quantitatively described by Hartree-Fock theory, suggest a divergent spin susceptibility at ${B}_{c}$ implying a ground state of minimum total spin just below ${B}_{c}$. In the spin polarized regime we observe a new phase also predicted by Hartree-Fock theory.

DOI
10.1103/physrevlett.74.785

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A droplet of N\ensuremath∼30N\ensuremath{\sim}30N\ensuremath∼30 electrons is created by lateral confinement of a two-dimensional electron gas. The evolution of its chemical potential \ensuremathμN{\ensuremath{\mu}}_{N}\ensuremathμN​ with magnetic field BBB is inferred from resonant tunneling experiments and is used to study the dependence of its magnetization on BBB.The experimental data, quantitatively described by Hartree-Fock theory, suggest a divergent spin susceptibility at Bc{B}_{c}Bc​ implying a ground state of minimum total spin just below Bc{B}_{c}Bc​. In the spin polarized regime we observe a new phase also predicted by Hartree-Fock theory.
The problem of the many-body enhancement of the static spin susceptibility at long wavelengths and its relation to the quasiparticle effective mass is investigated for a normal electron gas in two-dimensional space as a function of the electronic density. We start from a discussion of the results of the simple Hartree-Fock approximation for various interaction potentials and proceed to develop a complete theory. We find that the effects of the electron-electron interaction are significantly larger than in the familiar three-dimensional case. Our approach is based on a new self-consistent scheme which goes beyond the simple random-phase approximation by explicitly allowing for charge- and spin-fluctuation-induced vertex corrections of the Hubbard type. We show that when the latter are neglected, the many-body enhancement of the spin susceptibility can be cast in a remarkably simple and elegant analytic form.
The electronic structure of the ground state and some excited states of neutral atoms with the nuclear charge numbers 1< Z< 101<~Z<~101< Z< 10 and their singly positive ions are investigated by means of our two-dimensional mesh Hartree-Fock method for strong magnetic fields $0.5<~\ensuremath{\gamma}<~10000.$ For $\ensuremath{\gamma}=10000$ the ground-state configurations of all the atoms and ions considered are given by fully spin-polarized configurations of single-electron orbitals with magnetic quantum numbers ranging from m=0m=0m=0 to $m=\ensuremath{-}N+1,$ where N is the number of the electrons. Focusing on the fully spin-polarized situation, we provide critical values of the magnetic-field strength for which crossovers with respect to the spatial symmetries of the ground state take place. It is found that the neutral atoms and singly charged positive ions with 2< Z< 52<~Z<~52< Z< 5 have one fully spin-polarized ground-state configuration, whereas for 6< Z< 106<~Z<~106< Z< 10 one intermediate fully spin-polarized configuration with an orbital of 2p0{2p}_{0}2p0​ type occurs.
As a contribution to the study of the Hartree–Fock theory, we prove rigorously that the Hartree–Fock approximation to the ground state of the d-dimensional Hubbard model leads to saturated ferromagnetism when the particle density (more precisely, the chemical potential μ) is small and the coupling constant U is large, but finite. This ferromagnetism contradicts the known fact that there is no magnetization at low density, for any U, and thus shows that HF theory is wrong in this case. As in the usual Hartree–Fock theory, we restrict attention to Slater determinants that are eigenvectors of the z-component of the total spin, 𝕊z = ∑x nx,↑ - nx,↓, and we find that the choice 2𝕊z = N = particle number gives the lowest energy at fixed 0 < μ < 4d.
Using a combination of a fast two-dimensional-Hartree-Fock-Roothaan method and highly accurate fixed-phase diffusion quantum Monte Carlo simulations, we analyze the electronic structure and calculate the energy of the ground states of atoms with nuclear charges Z=2−−26Z=2--26Z=2−−26 in very strong magnetic fields $B={10}^{7}--5\ifmmode\times\else\texttimes\fi{}{10}^{8}\phantom{\rule{0.28em}{0ex}}\mathrm{T}$, relevant for astrophysical problems, e.g., the thermal emission of strongly magnetized isolated neutron stars.