skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Semiclassical model of a one-dimensional quantum dot

Abstract

A one-dimensional quantum dot at zero temperature is used as an example for developing a consistent semiclassical method. The method can also be applied to systems of higher dimension that admit separation of variables. For electrons confined by a quartic potential, the Thomas-Fermi approximation is used to calculate the self-consistent potential, the electron density distribution, and the total energy as a function of the electron number and the effective electron charge representing the strength of interaction between electrons. Use is made of scaling with respect to the electron number. An energy quantization condition is derived. The oscillating part of the electron density and both gradient and shell corrections to the total electron energy are calculated by using the results based on the Thomas-Fermi model and analytical expressions derived in this study. The dependence of the shell correction on the interaction strength is examined. Comparisons with results calculated by the density functional method are presented. The relationship between the results obtained and the Strutinsky correction is discussed.

Authors:
 [1]
  1. Russian Academy of Sciences, Institute of Mathematical Modeling (Russian Federation), E-mail: shpat@imamod.ru
Publication Date:
OSTI Identifier:
21067722
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Experimental and Theoretical Physics; Journal Volume: 102; Journal Issue: 3; Other Information: DOI: 10.1134/S1063776106030095; Copyright (c) 2006 Nauka/Interperiodica; Article Copyright (c) 2006 Pleiades Publishing, Inc; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CORRECTIONS; DENSITY FUNCTIONAL METHOD; ELECTRON DENSITY; ELECTRONS; FUNCTIONS; INTERACTIONS; ONE-DIMENSIONAL CALCULATIONS; POTENTIALS; QUANTIZATION; QUANTUM DOTS; SEMICLASSICAL APPROXIMATION; THOMAS-FERMI MODEL

Citation Formats

Shpatakovskaya, G. V.. Semiclassical model of a one-dimensional quantum dot. United States: N. p., 2006. Web. doi:10.1134/S1063776106030095.
Shpatakovskaya, G. V.. Semiclassical model of a one-dimensional quantum dot. United States. doi:10.1134/S1063776106030095.
Shpatakovskaya, G. V.. Wed . "Semiclassical model of a one-dimensional quantum dot". United States. doi:10.1134/S1063776106030095.
@article{osti_21067722,
title = {Semiclassical model of a one-dimensional quantum dot},
author = {Shpatakovskaya, G. V.},
abstractNote = {A one-dimensional quantum dot at zero temperature is used as an example for developing a consistent semiclassical method. The method can also be applied to systems of higher dimension that admit separation of variables. For electrons confined by a quartic potential, the Thomas-Fermi approximation is used to calculate the self-consistent potential, the electron density distribution, and the total energy as a function of the electron number and the effective electron charge representing the strength of interaction between electrons. Use is made of scaling with respect to the electron number. An energy quantization condition is derived. The oscillating part of the electron density and both gradient and shell corrections to the total electron energy are calculated by using the results based on the Thomas-Fermi model and analytical expressions derived in this study. The dependence of the shell correction on the interaction strength is examined. Comparisons with results calculated by the density functional method are presented. The relationship between the results obtained and the Strutinsky correction is discussed.},
doi = {10.1134/S1063776106030095},
journal = {Journal of Experimental and Theoretical Physics},
number = 3,
volume = 102,
place = {United States},
year = {Wed Mar 15 00:00:00 EST 2006},
month = {Wed Mar 15 00:00:00 EST 2006}
}
  • In this paper we study electronic transport through a quantum dot array containing an arbitrary number of quantum dots connected in a series by tunnel coupling under dc bias. The on-site Coulomb interaction is ignored. The retarded self-energy of any dot in the array is made up of left and right components and is of staircase type, terminating at corresponding electron reservoirs. We calculate the dc current based on the nonequilibrium Green{close_quote}s function formalism developed by Jauho et al. [A.-P. Jauho, Ned S. Wingreen, and Y. Meir, Phys. Rev. B >50, 5528 (1994)]. The dc current in both finite andmore » infinite number dots in the array is calculated. The electronic spectrum of the system is found to fall within an interval centered at {epsilon}{sub 0} (the dot energy level) with a width of two times the tunnel coupling amplitude between two neighboring dots. The electronic charge in each dot is plotted for the finite number dot array.« less
  • A set of rules is given for dealing with WKB expansions in the one-dimensional analytic case, whereby such expansions are not considered as approximations but as exact encodings of wave functions, thus allowing for analytic continuation with respect to whichever parameters the potential function depends on, with an exact control of small exponential effects. These rules, which include also the case when there are double turning points, are illustrated on various examples, and applied to the study of bound state or resonance spectra. In the case of simple oscillators, it is thus shown that the Rayleigh{endash}Schr{umlt o}dinger series is Borelmore » resummable, yielding the exact energy levels. In the case of the symmetrical anharmonic oscillator, one gets a simple and rigorous justification of the Zinn-Justin quantization condition, and of its solution in terms of {open_quotes}multi-instanton expansions.{close_quotes} {copyright} {ital 1997 American Institute of Physics.}« less
  • We demonstrate the selective optical excitation and detection of subsets of quantum dots (QDs) within an InAs/InP ensemble using a SiO{sub 2}/Ta{sub 2}O{sub 5}-based optical microcavity. The low variance of the exciton transition energy and dipole moment tied to the narrow linewidth of the microcavity mode is expected to facilitate effective qubit encoding and manipulation in a quantum dot ensemble with ease of quantum state readout relative to qubits encoded in single quantum dots.
  • We present theoretical investigations of miniband structures and optical properties of InAs/GaAs one-dimensional quantum dot superlattices (1D-QDSLs). The calculation is based on the multi-band k·p theory, including the conduction and valence band mixing effects, the strain effect, and the piezoelectric effect; all three effects have periodic boundary conditions. We find that both the electronic and optical properties of the 1D-QDSLs show unique states which are different from those of well known single quantum dots (QDs) or quantum wires. We predict that the optical absorption spectra of the 1D-QDSLs strongly depend on the inter-dot spacing because of the inter-dot carrier couplingmore » and changing strain states, which strongly influence the conduction and valence band potentials. The inter-miniband transitions form the absorption bands. Those absorption bands can be tuned from almost continuous (closely stacked QD case) to spike-like shape (almost isolated QD case) by changing the inter-dot spacing. The polarization of the lowest absorption peak for the 1D-QDSLs changes from being parallel to the stacking direction to being perpendicular to the stacking direction as the inter-dot spacing increases. In the case of closely stacked QDs, in-plane anisotropy, especially [110] and [11{sup ¯}0] directions also depend on the inter-dot spacing. Our findings and predictions will provide an additional degree of freedom for the design of QD-based optoelectronic devices.« less
  • The penetration through a two dimensional fission barrier is investigated by a fully quantum mechanical coupled channel calculation and by a new semiclassical method. One finds a quantitative agreement. (auth)