53 research outputs found
Density functional theory of the phase diagram of maximum density droplets in two-dimensional quantum dots in a magnetic field
We present a density-functional theory (DFT) approach to the study of the
phase diagram of the maximum density droplet (MDD) in two-dimensional quantum
dots in a magnetic field. Within the lowest Landau level (LLL) approximation,
analytical expressions are derived for the values of the parameters (number
of electrons) and (magnetic field) at which the transition from the MDD to
a ``reconstructed'' phase takes place. The results are then compared with those
of full Kohn-Sham calculations, giving thus information about both correlation
and Landau level mixing effects. Our results are also contrasted with those of
Hartree-Fock (HF) calculations, showing that DFT predicts a more compact
reconstructed edge, which is closer to the result of exact diagonalizations in
the LLL.Comment: ReVTeX 3.
Broken Symmetries in the Reconstruction of v=1 Quantum Hall Edges
Spin-polarized reconstruction of the v=1 quantum Hall edge is accompanied by
a spatial modulation of the charge density along the edge. We find that this is
also the case for finite quantum Hall droplets: current spin density functional
calculations show that the so-called Chamon-Wen edge forms a ring of apparently
localized electrons around the maximum density droplet (MDD). The boundaries of
these different phases qualitatively agree with recent experiments. For very
soft confinement, Chern-Simons Ginzburg-Landau theory indicates formation of a
non-translational invariant edge with vortices (holes) trapped in the edge
region.Comment: Proceedings of the EP2DS, Ottawa (1999) (submitted to Physica E
Current Density Functional approach to large quantum dots in intense magnetic fields
Within Current Density Functional Theory, we have studied a quantum dot made
of 210 electrons confined in a disk geometry. The ground state of this large
dot exhibits some features as a function of the magnetic field (B) that can be
attributed in a clear way to the formation of compressible and incompressible
states of the system. The orbital and spin angular momenta, the total energy,
ionization and electron chemical potentials of the ground state, as well as the
frequencies of far-infrared edge modes are calculated as a function of B, and
compared with available experimental and theoretical results.Comment: Typeset using Revtex, 17 pages and 13 Postscript figure
Current-spin-density functional study of persistent currents in quantum rings
We present a numerical study of persistent currents in quantum rings using
current spin density functional theory (CSDFT). This formalism allows for a
systematic study of the joint effects of both spin, interactions and impurities
for realistic systems. It is illustrated that CSDFT is suitable for describing
the physical effects related to Aharonov-Bohm phases by comparing energy
spectra of impurity-free rings to existing exact diagonalization and
experimental results. Further, we examine the effects of a symmetry-breaking
impurity potential on the density and current characteristics of the system and
propose that narrowing the confining potential at fixed impurity potential will
suppress the persistent current in a characteristic way.Comment: 7 pages REVTeX, including 8 postscript figure
Structure and far-infrared edge modes of quantum antidots at zero magnetic field
We have investigated edge modes of different multipolarity sustained by
quantum antidots at zero magnetic field. The ground state of the antidot is
described within a local density functional formalism. Two sum rules, which are
exact within this formalism, have been derived and used to evaluate the energy
of edge collective modes as a function of the surface density and the size of
the antidot.Comment: Typeset using Revtex, 8 pages and 6 Postscript figure
Ensemble density functional theory of the fractional quantum Hall effect
We develop an ensemble density functional theory for the fractional quantum
Hall effect using a local density approximation. Model calculations for edge
reconstructions of a spin-polarized quantum dot give results in good agreement
with semiclassical and Hartree-Fock calculations, and with small system
numerical diagonalizations. This establishes the usefulness of density
functional theory to study the fractional quantum Hall effect, which opens up
the possibility of studying inhomegeneous systems with many more electrons than
has heretofore been possible.Comment: Improved discussion of ensemble density functional theory. 4 pages
plus 3 postscript figures, uses latex with revtex. Contact
[email protected]
Far-infrared edge modes in quantum dots
We have investigated edge modes of different multipolarity sustained by
quantum dots submitted to external magnetic fields. We present a microscopic
description based on a variational solution of the equation of motion for any
axially symmetric confining potential and multipole mode. Numerical results for
dots with different number of electrons whose ground-state is described within
a local Current Density Functional Theory are discussed. Two sum rules, which
are exact within this theory, are derived. In the limit of a large neutral dot
at B=0, we have shown that the classical hydrodynamic dispersion law for edge
waves \omega(q) \sim \sqrt{q \ln (q_0/q)} holds when quantum and finite size
effects are taken into account.Comment: We have changed some figures as well as a part of the tex
Far-infrared edge modes in quantum dots
We have investigated edge modes of different multipolarity sustained by
quantum dots submitted to external magnetic fields. We present a microscopic
description based on a variational solution of the equation of motion for any
axially symmetric confining potential and multipole mode. Numerical results for
dots with different number of electrons whose ground-state is described within
a local Current Density Functional Theory are discussed. Two sum rules, which
are exact within this theory, are derived. In the limit of a large neutral dot
at B=0, we have shown that the classical hydrodynamic dispersion law for edge
waves \omega(q) \sim \sqrt{q \ln (q_0/q)} holds when quantum and finite size
effects are taken into account.Comment: We have changed some figures as well as a part of the tex
Pade approximants for the ground-state energy of closed-shell quantum dots
Analytic approximations to the ground-state energy of closed-shell quantum
dots (number of electrons from 2 to 210) are presented in the form of two-point
Pade approximants. These Pade approximants are constructed from the small- and
large-density limits of the energy. We estimated that the maximum error,
reached for intermediate densities, is less than 3%. Within the present
approximation the ground-state is found to be unpolarized.Comment: 4 pages, RevTeX, 3 ps figure
An exchange-correlation energy for a two-dimensional electron gas in a magnetic field
We present the results of a variational Monte Carlo calculation of the
exchange-correlation energy for a spin-polarized two-dimensional electron gas
in a perpendicular magnetic field. These energies are a necessary input to the
recently developed current-density functional theory. Landau-level mixing is
included in a variational manner, which gives the energy at finite density at
finite field, in contrast to previous approaches. Results are presented for the
exchange-correlation energy and excited-state gap at 1/7, 1/5, 1/3, 1,
and 2. We parameterize the results as a function of and in a form
convenient for current-density functional calculations.Comment: 36 pages, including 6 postscript figure
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