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Physical review. B, Condensed matter

Four-electron quantum dot in a magnetic field

M. B. Tavernier, Egidijus Anisimovas, François Maria Peeters, B. Szafran, Janusz Adamowski, S. Bednarek

Published Nov 12, 2003• 101 citations
Publisher

Abstract

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.

DOI
10.1103/physrevb.68.205305

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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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The exact diagonalization technique is used to study many-particle properties of interacting electrons with spin, confined in a two-dimensional harmonic potential. The single-particle basis is limited to the lowest Landau level. The results are analysed as a function of the total angular momentum of the system. Only at angular momenta corresponding to the filling factors 1, 1/3, 1/5, etc is the system fully polarized. The lowest energy states exhibit spin waves, domains, and localization, depending on the angular momentum. Vortices exist only at excited polarized states. The high angular momentum limit shows localization of electrons and separation of the charge and spin excitations.
This thesis investigates the use of wave-function methods for the study of quantum-dot systems. It investigates single dots, using quantum Monte Carlo techniques in a wide range of magnetic field values, and a double-dot system, using the exact-diagonalization method.\n\nThe thesis proposes simple yet accurate many-particle wave functions for various angular-momentum and spin states, for both weak and strong magnetic fields. Using these trial wave functions, it evaluates various properties of dots and studies Wigner crystallization and spin polarization for the weak-field limit. For strong magnetic fields, the thesis investigates ground states of different spin polarizations as a function of the magnetic field and tests the commonly used lowest-Landau-level approximation. The results are compared to calculations from the density-functional theory.\n\nFinally, the thesis presents a method that combines the accuracy of the exact-diagonalization method and the scalability of Monte Carlo methods. The Monte Carlo-based diagonalization is a promising tool for use in situations that cannot be handled with a simple trial wave function, and have too many particles for an exact-diagonalization treatment. For quantum dots, methods for efficiently evaluating the high-magnetic-field basis functions and their gradients are demonstrated.
The electron-electron correlations in a many-electron (Ne=1,2,…,5)({N}_{e}=1,2,\dots{},5)(Ne​=1,2,…,5) quantum dot confined by a parabolic potential is investigated in the presence of a single magnetic ion and a perpendicular magnetic field. We obtained the energy spectrum and calculated the addition energy which exhibits cusps as a function of the magnetic field. The vortex properties of the many-particle wave function of the ground state are studied and for large magnetic fields are related to composite fermions. The position of the impurity influences strongly the spin-pair-correlation function when the external field is large. In a small applied magnetic field, the spin-exchange energy together with the Zeeman terms leads to a ferromagnetic-antiferromagnetic (FM-AFM) transition. When the magnetic ion is shifted away from the center of the quantum dot, a remarkable re-entrant AFM-FM-AFM transition is found as a function of the strength of the Coulomb interaction. Thermodynamic quantities such as the heat capacity, the magnetization, and the susceptibility are also studied. The cusps in the energy levels show up as peaks in the heat capacity and the susceptibility.