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Physical Review B

Interacting electrons in one-dimensional quantum rings in a threading magnetic field: Spin phases and correlation

Stefano Bellucci A, Pasquale Onorato

Published Nov 24, 2009• 5 citations
Publisher

Abstract

We study ${N}_{e}$ interacting electrons confined in a one-dimensional quantum ring (QR) first by using a Hartree-Fock approximation and then by introducing correlation effects. An external magnetic field $B$ perpendicular to the ring plane is considered. The energy spectra of low-lying states of the QR as a function of $B$ and ${N}_{e}$ are obtained. A phase diagram is presented indicating a rich variety of ground states. By plotting the density functions of the QR, the ground-state configuration is found to be a regular polygon.

DOI
10.1103/physrevb.80.195115

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We study Ne{N}_{e}Ne​ interacting electrons confined in a one-dimensional quantum ring (QR) first by using a Hartree-Fock approximation and then by introducing correlation effects. An external magnetic field BBB perpendicular to the ring plane is considered. The energy spectra of low-lying states of the QR as a function of BBB and Ne{N}_{e}Ne​ are obtained. A phase diagram is presented indicating a rich variety of ground states. By plotting the density functions of the QR, the ground-state configuration is found to be a regular polygon.
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We present a theoretical treatment of four two-dimensional electrons in a harmonic confinement potential in the presence of an external magnetic field using the exact diagonalization approach. The ground state properties and the spin and angular momentum transitions for different electron interaction strengths and magnetic fields are obtained. A magnetic field-confinement strength phase diagram is presented indicating a rich variety of ground states. An interesting feature of this system is the depolarization of spins by application of a magnetic field. The results are compared to several approximate theories.
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Dynamical response theory is employed to investigate the effects of various transverse confinements on electron correlations in the ground state of a ferromagnetic one-dimensional quantum wire for different wire widths b and density parameters r s . In the regime of a thin quantum wire, electrons are treated as a one-dimensional gas under different confinement models via effective electron-electron interaction potentials. Using the first-order random phase approximation (FRPA) including self-energy and exchange contribution, which provides the ground-state structure beyond the random phase approximation, we numerically compute the structure factor, pair-correlation function, correlation energy, and ground-state energy for various values of b and r s . Our results reveal that the correlation energy depends on the choice of confinement model. For the ultrathin wire ( b → 0 ) in the high-density limit, we find that the correlation energy for transverse confinement models V 1 ( q ) (harmonic), V 2 ( q ) (cylindrical), and V 5 ( q ) (harmonic-delta) approaches ε c ( r s ) = − π 2 / 360 ∼ − 0.02741 a.u., which agrees with the exact results in this limit [P.-F. Loos, ; V. Ashokan, , ]. This clearly illustrates that for at least these three confinement potentials, the one-dimensional Coulomb potential can be regularized at interparticle distance x = 0 to yield the same correlation energy. In contrast, other confinement potentials, V 3 ( q ) (infinite square well), V 4 ( q ) (infinite square-infinite triangular well), and V 6 ( q ) (infinite square-delta well), do not approach the same high-density limit; instead, the correlation energy tends to ε c ∼ − 0.03002 a.u. for these potentials. The percentage difference in correlation energy between the confinement models V 1 ( q ) , V 2 ( q ) , V 5 ( q ) and V 3 ( q ) ,
Background: Idealized systems are commonly used in nuclear physics and condensed matter. For instance, the construction of nuclear energy density functionals involves properties of infinite matter, whereas neutron drops are used to test nuclear interactions and approximations to the nuclear many-body problem. In condensed matter, quantum rings are also used to study properties of electron systems.Purpose: To investigate the possibility to use quantum rings with systems of nucleons including many-body correlations.Methods: A quantum ring model of a finite number of same spin fermions is developed. Several attractive and repulsive interactions with finite and infinite ranges are considered. Quantum Monte Carlo calculations are used to provide exact ground-state energies. Comparisons with analytical Hartree-Fock solutions are used to get an insight into the role of correlations.Results: Hartree-Fock results with no breaking of space translational symmetry are able to describe many systems. However, additional spatial correlations are required in the case of dense systems with a strong short-range repulsion or with attractive interactions in large rings.Conclusions: Self-bound systems of fermions with spatial correlations produced by basic features of the nuclear interactions can be described on a quantum ring, encouraging applications with realistic interactions, as well as investigations with higher-dimensional geometries, such as spherium.