A parabolic quantum dot with N electrons and an impurity (original) (raw)
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Physica E-low-dimensional Systems & Nanostructures, 2004
The two dimensional Thomas-Fermi approximation is applied to the problem of parabolic quantum dot composed of N electrons and an on-center impurity. Change induced by impurity on electron density, chemical potential and total energy is discussed and it is found that existence of impurity makes significant changes on the determination of above properties especially for the small number of electrons and strong confinements.
2006
The effect of number of particles on the physical properties of a two dimensional parabolic quantum dot system is investigated numerically at finite temperature. The Thomas-Fermi equation is solved self consistently with Poisson equation. The changes induced by electron-electron interaction are also analyzed. It is shown that the numerical procedure that is applied to solve the problem is very efficient at all temperatures.
Confinement Characterization of a 2-Electron Quantum Dot
The time independent Schoedinger equation for two electrons confined in a parabolic external potential is solved. Developing this solution in terms of a dimensionless variable it is demonstrated that parameterization of the strength of the confining potential separate from the effective mass assumption greatly clarifies the functional dependence of the system energy on the system parameters. The determination of the strength of the external confinement and validation of the effective mass assumption in real devices is greatly improved by characterizing the strength of the confining potential separate from the effective mass. Comment: 13 pages, pdf format
Quantum and Classical Calculations of Ground State Properties of Parabolic Quantum Dots
2005
We report calculations for electronic ground states of parabolically confined quantum dots for up to 30 electrons based on the quantum Monte Carlo method. Effects of the electron-electron interaction and the response to a magnetic field are exposed. The wavefunctions and the ground state energies are compared with purely classical calculations performed with a comprehensive Molecular Dynamics code. For the chosen well parameters a close correspondence in the overall shape of electron density distribution is found even for small number of electrons, while the detailed radial distributions show the effects of Pauli principle in the quantal case.
Optical properties of two-dimensional two-electron quantum dot in parabolic confinement
Open Physics
The Hamiltonian and wavefunctions of two-dimensional two-electron quantum dots (2D2eQD) in parabolic confinement are determined. The ground and excited state energies are calculated solving the Schrödinger equation analytically and numerically. To determine the energy eigen-value of the system variational method is employed due to the large coupling constant λ ≈ 1.1 \lambda \approx 1.1 . The trial wavefunctions are developed for both ground and excited states. The ground state wave function is a para state and the excited state wavefunctions belong to both para and ortho states based on the symmetry and antisymmetry of spatial wavefunctions. Using the obtained energy eigen-values at the two states, the first- and third-order nonlinear absorption coefficient and refractive index are analytically obtained with the help of density matrix formalism and iterative procedure.
On the confinement potential formation in a two-electron quantum dot
Journal of Experimental and Theoretical Physics, 2001
A model of a quantum dot for two interacting electrons is proposed and analyzed. The properties of the ambient determining the form of the confinement potential for electrons are simulated using the electrostatic field of the image charge. Analytic expressions for the eigenvalues of each subsystem are derived taking into account the external magnetic field and using the representation of the system Hamiltonian as the sum of the Hamiltonians of the center of mass and of relative motion on the basis of the method of oscillator representation [M. Dineykhan and G. V. Efimov, Element. ]. The relative motion of electrons is responsible for a confinement potential which differs from the parabolic confinement potential and is a function of the electron effective mass as well as the characteristics of the image charge. © 2001 MAIK "Nauka/Interperiodica".
Two Electrons in a Quantum Dot: A Unified Approach
International Journal of Theoretical Physics, 2008
Low-lying energy levels of two interacting electrons confined in a two-dimensional parabolic quantum dot in the presence of an external magnetic field have been revised within the frame of a novel model. The present formalism, which gives closed algebraic solutions for the specific values of magnetic field and spatial confinement length, enables us to see explicitly individual effects of the electron correlation.
Classical behavior of few-electron parabolic quantum dots
Physica B: Condensed Matter, 2009
Quantum dots are intricate and fascinating systems to study novel phenomena of great theoretical and practical interest because low dimensionality coupled with the interplay between strong correlations, quantum confinement and magnetic field creates unique conditions for emergence of fundamentally new physics. In this work we consider two-dimensional semiconductor quantum dot systems consisting of few interacting electrons confined in an isotropic parabolic potential. We study the many-electron quantum ground state properties of such systems in presence of a perpendicular magnetic field as the number of electrons is varied using exact numerical diagonalizations and other approaches. The results derived from the calculations of the quantum model are then compared to corresponding results for a classical model of parabolically confined point charges who interact with a Coulomb potential. We find that, for a wide range of parameters and magnetic fields considered in this work, the quantum ground state energy is very close to the classical energy of the most stable classical configuration under the condition that the classical energy is properly adjusted to incorporate the quantum zero point motion.
Journal of the Korean Physical Society, 2018
In this work, the ground-state properties of an interacting electron gas confined in a twodimensional quantum dot system with the Gaussian potential υ(r) = V0(1 − exp(−r 2 /p)), where V0 and p are confinement parameters, are determined numerically by using the Thomas-Fermi approximation. The shape of the potential is modified by changing the V0 and the p values, and the influence of the confining potential on the system's properties, such as the chemical energy, the density profile, the kinetic energy, the confining energy, etc., is analyzed for both the non-interacting and the interacting cases. The results are compared with those calculated for a harmonic potential, and excellent agreement is obtained in the limit of high p values for both the non-interacting and the interacting cases.
Numerical study of 2-D quantum dots
We present a numerical study of the chemical potential and of the capacitance in a model quantum dot. Our model includes the electron-electron interaction and exchange and correlation effects within the framework of density functional theory. Our results exhibit the typical features observed in experiments, such as the increase in the capacitance for increasing number of electrons and the presence of irregularities in the succession of the chemical potential values vs. the electron number.