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Physical review. B, Condensed matter

Disordered quantum dots: A diffusion quantum Monte Carlo study

Alev Devrim Güçlü, Jian‐Sheng Wang, Hong Min Guo

Published Jul 2, 2003• 22 citations
Publisher

Abstract

We report diffusion quantum Monte Carlo (DQMC) calculations of disordered quantum dots in the presence of an external magnetic field. The addition spectra, spin configuration, Hund's rule, and many-body densities are investigated up to 13 electrons. The data from DQMC is in excellent agreement with exact diagonalization for disorder-free quantum dots, and in marked difference with those obtained from unrestricted Hartree-Fock method. The energetic competition to electron-electron interaction due to disorder is found to change the transition energy between spin states, but the closed shell Hund's rule is maintained for the disorder strength considered here. The DQMC many-body density is found to be rather smooth.

DOI
10.1103/physrevb.68.035304

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We report diffusion quantum Monte Carlo (DQMC) calculations of disordered quantum dots in the presence of an external magnetic field. The addition spectra, spin configuration, Hund's rule, and many-body densities are investigated up to 13 electrons. The data from DQMC is in excellent agreement with exact diagonalization for disorder-free quantum dots, and in marked difference with those obtained from unrestricted Hartree-Fock method. The energetic competition to electron-electron interaction due to disorder is found to change the transition energy between spin states, but the closed shell Hund's rule is maintained for the disorder strength considered here. The DQMC many-body density is found to be rather smooth.
We explore the correlated electron states in harmonically confined few-electron quantum dots in an external magnetic field by the path-integral Monte Carlo method for a wide range of the field and the Coulomb interaction strength. Using the phase structure of a preceding unrestricted Hartree-Fock calculation for phase fixing, we find a rich variety of correlated states, often completely different from the prediction of mean-field theory. These are finite temperature results, but sometimes the correlations saturate with decreasing temperature, providing insight into the ground-state properties.
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.
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.
We introduce a generic approach to study interaction effects in diffusive or chaotic quantum dots in the Coulomb blockade regime. The randomness of the single-particle wave functions induces randomness in the two-body interaction matrix elements. We classify the possible induced two-body ensembles, both in the presence and absence of spin degrees of freedom. The ensembles depend on the underlying space-time symmetries as well as on features of the two-body interaction. Confining ourselves to spinless electrons, we then use the Hartree-Fock (HF) approximation to calculate HF single-particle energies and HF wave functions for many realizations of the ensemble. We study the statistical properties of the resulting one-body HF ensemble for a fixed number of electrons. In particular, we determine the statistics of the interaction matrix elements in the HF basis, of the HF single-particle energies (including the HF gap between the last occupied and the first empty HF level), and of the HF single-particle wave functions. We also study the addition of electrons, and in particular the distribution of the distance between successive conductance peaks and of the conductance peak heights.
A system of N=2--4 interacting electrons in a quantum dot, with applied magnetic field, is treated using a quantum Monte Carlo method. The standard fixed-node Monte Carlo approach is modified to facilitate the inclusion of a magnetic field giving rise to a fixed-phase approximation which is introduced here. By making use of this approximation, results whose accuracy is comparable to that of exact diagonalization can be obtained. A simple set of coordinates for the four-particle problem is also used which facilitates finding a symmetrized basis. \textcopyright{} 1996 The American Physical Society.
We use a variational Monte Carlo algorithm to solve the electronic structure of two-dimensional semiconductor quantum dots in external magnetic field. We present accurate many-body wave functions for the system in various magnetic field regimes. We show the importance of symmetry, and demonstrate how it can be used to simplify the variational wave functions. We present in detail the algorithm for efficient wave function optimization. We also present a Monte Carlo-based diagonalization technique to solve the quantum dot problem in the strong magnetic field limit where the system is of a multiconfiguration nature. PACS numbers: 71.10.-w, 73.21.La, 02.70.Ss 1.