110 research outputs found
Distortion of Wigner molecules : pair function approach
We considered a two dimensional three electron quantum dot in a magnetic
field in the Wigner limit. A unitary coordinate transformation decouples the
Hamiltonian (with Coulomb interaction between the electrons included) into a
sum of three independent pair Hamiltonians. The eigen-solutions of the pair
Hamiltonian provide a spectrum of pair states. Each pair state defines the
distance of the two electrons involved in this state. In the ground state for
given pair angular momentum , this distance increases with increasing .
The pair states have to be occupied under consideration of the Pauli exclusion
principle, which differs from that for one-electron states and depends on the
total spin and the total orbital angular momentum (sum over
all pair angular momenta). We have shown that the three electrons in the ground
state of the Wigner molecule form an equilateral triangle (as might be
expected) only, if the state is a quartet () and the orbital angular
momentum is a magic quantum number ( integer). Otherwise the
triangle in the ground state is isosceles. For one of the sides is
longer and for one of the sides is shorter than the other two
Wigner Crystallization of a two dimensional electron gas in a magnetic field: single electrons versus electron pairs at the lattice sites
The ground state energy and the lowest excitations of a two dimensional
Wigner crystal in a perpendicular magnetic field with one and two electrons per
cell is investigated. In case of two electrons per lattice site, the
interaction of the electrons {\em within} each cell is taken into account
exactly (including exchange and correlation effects), and the interaction {\em
between} the cells is in second order (dipole) van der Waals approximation. No
further approximations are made, in particular Landau level mixing and {\em
in}complete spin polarization are accounted for. Therefore, our calculation
comprises a, roughly speaking, complementary description of the bubble phase
(in the special case of one and two electrons per bubble), which was proposed
by Koulakov, Fogler and Shklovskii on the basis of a Hartree Fock calculation.
The phase diagram shows that in GaAs the paired phase is energetically more
favorable than the single electron phase for, roughly speaking, filling factor
larger than 0.3 and density parameter smaller than 19 effective Bohr
radii (for a more precise statement see Fig.s 4 and 5). If we start within the
paired phase and increase magnetic field or decrease density, the pairs first
undergo some singlet- triplet transitions before they break.Comment: 11 pages, 7 figure
Quasi-exact solutions for two interacting electrons in two-dimensional anisotropic dots
We present an analysis of the two-dimensional Schrodinger equation for two
electrons interacting via Coulombic force and confined in an anizotropic
harmonic potential. The separable case of wy = 2wx is studied particularly
carefully. The closed-form expressions for bound-state energies and the
corresponding eigenfunctions are found at some particular values of wx. For
highly-accurate determination of energy levels at other values of wx, we apply
an efficient scheme based on the Frobenius expansion.Comment: 11 pages, 4 figure
Unpaired and spin-singlet paired states of a two-dimensional electron gas in a perpendicular magnetic field
We present a variational study of both unpaired and spin-singlet paired
states induced in a two-dimensional electron gas at low density by a
perpendicular magnetic field. It is based on an improved circular-cell
approximation which leads to a number of closed analytical results. The
ground-state energy of the Wigner crystal containing a single electron per cell
in the lowest Landau level is obtained as a function of the filling factor
: the results are in good agreement with those of earlier approaches and
predict for the upper filling factor at which the
solid-liquid transition occurs. A novel localized state of spin-singlet
electron pairs is examined and found to be a competitor of the unpaired state
for filling factor . The corresponding phase boundary is quantitatively
displayed in the magnetic field-electron density plane.Comment: 19 pages, 8 figures, submitted to Phys. Rev. B on 7th April 2001. to
appear in Phys. Rev.
Quantum-dot lithium in zero magnetic field: Electronic properties, thermodynamics, and a liquid-solid transition in the ground state
Energy spectra, electron densities, pair correlation functions and heat
capacity of a quantum-dot lithium in zero external magnetic field (a system of
three interacting two-dimensional electrons in a parabolic confinement
potential) are studied using the exact diagonalization approach. A particular
attention is given to a Fermi-liquid -- Wigner-solid transition in the ground
state of the dot, induced by the intra-dot Coulomb interaction.Comment: 12 pages, incl. 16 figure
Roto-vibrational spectrum and Wigner crystallization in two-electron parabolic quantum dots
We provide a quantitative determination of the crystallization onset for two
electrons in a parabolic two-dimensional confinement. This system is shown to
be well described by a roto-vibrational model, Wigner crystallization occurring
when the rotational motion gets decoupled from the vibrational one. The Wigner
molecule thus formed is characterized by its moment of inertia and by the
corresponding sequence of rotational excited states. The role of a vertical
magnetic field is also considered. Additional support to the analysis is given
by the Hartree-Fock phase diagram for the ground state and by the random-phase
approximation for the moment of inertia and vibron excitations.Comment: 10 pages, 8 figures, replaced by the published versio
Planar Dirac Electron in Coulomb and Magnetic Fields
The Dirac equation for an electron in two spatial dimensions in the Coulomb
and homogeneous magnetic fields is discussed. For weak magnetic fields, the
approximate energy values are obtained by semiclassical method. In the case
with strong magnetic fields, we present the exact recursion relations that
determine the coefficients of the series expansion of wave functions, the
possible energies and the magnetic fields. It is found that analytic solutions
are possible for a denumerably infinite set of magnetic field strengths. This
system thus furnishes an example of the so-called quasi-exactly solvable
models. A distinctive feature in the Dirac case is that, depending on the
strength of the Coulomb field, not all total angular momentum quantum number
allow exact solutions with wavefunctions in reasonable polynomial forms.
Solutions in the nonrelativistic limit with both attractive and repulsive
Coulomb fields are briefly discussed by means of the method of factorization.Comment: 18 pages, RevTex, no figure
Formation and control of electron molecules in artificial atoms: Impurity and magnetic-field effects
Interelectron interactions and correlations in quantum dots can lead to
spontaneous symmetry breaking of the self-consistent mean field resulting in
formation of Wigner molecules. With the use of spin-and-space unrestricted
Hartree-Fock (sS-UHF) calculations, such symmetry breaking is discussed for
field-free conditions, as well as under the influence of an external magnetic
field. Using as paradigms impurity-doped (as well as the limiting case of
clean) two-electron quantum dots (which are analogs to helium-like atoms), it
is shown that the interplay between the interelectron repulsion and the
electronic zero-point kinetic energy leads, for a broad range of impurity
parameters, to formation of a singlet ground-state electron molecule,
reminiscent of the molecular picture of doubly-excited helium. Comparative
analysis of the conditional probability distributions for the sS-UHF and the
exact solutions for the ground state of two interacting electrons in a clean
parabolic quantum dot reveals that both of them describe formation of an
electron molecule with similar characteristics. The self-consistent field
associated with the triplet excited state of the two-electron quantum dot
(clean as well as impurity-doped) exhibits symmetry breaking of the Jahn-Teller
type, similar to that underlying formation of nonspherical open-shell nuclei
and metal clusters. Furthermore, impurity and/or magnetic-field effects can be
used to achieve controlled manipulation of the formation and pinning of the
discrete orientations of the Wigner molecules. Impurity effects are futher
illustrated for the case of a quantum dot with more than two electrons.Comment: Latex/Revtex, 10 pages with 4 gif figures. Small changes to explain
the difference between Wigner and Jahn-Teller electron molecules. A complete
version of the paper with high quality figures inside the text is available
at http://shale.physics.gatech.edu/~costas/qdhelium.html For related papers,
see http://www.prism.gatech.edu/~ph274c
Exchange-correlation vector potentials and vorticity-dependent exchange-correlation energy densities in two-dimensional systems
We present a new approach how to calculate the scalar exchange-correlation
potentials and the vector exchange-correlation potentials from current-carrying
ground states of two-dimensional quantum dots. From these exchange-correlation
potentials we derive exchange-correlation energy densities and examine their
vorticity (or current) dependence. Compared with parameterizations of
current-induced effects in literature we find an increased significance of
corrections due to paramagnetic current densities.Comment: 5 figures, submitted to PR
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