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arXiv:cond-mat/0112243 · Physical review. B, Condensed matter

Various spin-polarization states beyond the maximum-density droplet: A quantum Monte Carlo study

Sami Siljamaki, Ari Harju, R. M. Nieminen, Viktor A. Sverdlov, Petteri Hyvönen

Published Mar 12, 2002• 22 citations
arXivHTMLPDF

Abstract

Using a variational quantum Monte Carlo method, the effect of Landau-level mixing on the lowest-energy--state diagram of small quantum dots is studied in the magnetic-field range where the density of magnetic flux quanta just exceeds the density of electrons. An accurate analytical many-body wave function is constructed for various angular momentum and spin states in the lowest Landau level, and Landau-level mixing is then introduced using a Jastrow factor. The effect of higher Landau levels is shown to be significant; the transition lines are shifted considerably towards higher values of magnetic field and certain lowest-energy states vanish altogether.

DOI
10.1103/physrevb.65.121306

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Using a variational quantum Monte Carlo method, the effect of Landau-level mixing on the lowest-energy--state diagram of small quantum dots is studied in the magnetic-field range where the density of magnetic flux quanta just exceeds the density of electrons. An accurate analytical many-body wave function is constructed for various angular momentum and spin states in the lowest Landau level, and Landau-level mixing is then introduced using a Jastrow factor. The effect of higher Landau levels is shown to be significant; the transition lines are shifted considerably towards higher values of magnetic field and certain lowest-energy states vanish altogether.
An efficient variational many-body wave function for electrons in a quantum dot is introduced. We show that the proposed bosonic two-body correlation factor is able to capture nearly exactly the missing correlations of the lowest-Landau-level many-body wave function. We compare the results with exact diagonalizations. The comparison shows that quantum Monte Carlo techniques combined with the proposed wave function are a powerful tool for studying quantum dots. As further evidence for this, we apply the scheme to a maximum density droplet state for up to 40 electrons.
A variational method of calculating the spin 1 excitation energies of the $\ensuremath{\nu}=1$ quantum Hall liquid is presented in detail. We are able to include Landau-level mixing and finite-thickness effects. The many-body wave functions of the states near $\ensuremath{\nu}=1$ filling are taken to be a product of a lowest-Landau-level Laughlin-type wave function and a Jastrow factor. A significant reduction in the calculated spin gap is found due both to Landau-level mixing $(\ensuremath{\sim}40%$ at rs=1){r}_{s}=1)rs​=1) and to the effect of the finite thickness of the liquid (a further $\ensuremath{\sim}30%$ at rs=1){r}_{s}=1)rs​=1). We find our calculations to be consistent with recent photoluminescence experiments in $\ensuremath{\delta}$-doped samples.
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 ground states of parabolically confined electrons in a quantum dot are studied by both direct numerical diagonalization and quantum Monte Carlo (QMC) methods. We present a simple but accurate variational many-body wave function for the dot in the limit of a weak magnetic field. The wave function has the center-of-mass motion restricted to the lowest-energy state and the electron-electron interaction is taken into account by a Jastrow two-body correlation factor. The optimized wave function has an accuracy very close to the state-of-the-art numerical diagonalization calculations. The results and the computational efficiency indicate that the presented wave function combined with the QMC method suits ideally for studies of large quantum dots.
We calculate the ground-state energy and the effective spin Land\'e g factor (g∗{\mathit{g}}^{\mathrm{*}}g∗) of a two-dimensional electron gas in strong magnetic fields using a variational Monte Carlo method and many-body trial wave functions composed of the Jastrow correlation factor and the Laughlin-type functions. We find that g∗{\mathit{g}}^{\mathrm{*}}g∗ increases with decreasing of electron density and also shows increasing behavior as the filling factor \ensuremath{\nu} decreases in the region of 12. At \ensuremath{\nu}=1.0, g∗{\mathit{g}}^{\mathrm{*}}g∗ is estimated to be about 11 for a dimensionless parameter rs{\mathit{r}}_{\mathit{s}}rs​=1.33, as compared to the measured value of 7.3, while considering impurity and phonon scatterings gives a better agreement of g∗{\mathit{g}}^{\mathrm{*}}g∗=9. \textcopyright{} 1996 The American Physical Society.