118 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
Solution of the Schr\"odinger Equation for Quantum Dot Lattices with Coulomb Interaction between the Dots
The Schr\"odinger equation for quantum dot lattices with non-cubic,
non-Bravais lattices built up from elliptical dots is investigated. The Coulomb
interaction between the dots is considered in dipole approximation. Then only
the center of mass (c.m.) coordinates of different dots couple with each other.
This c.m. subsystem can be solved exactly and provides magneto- phonon like
collective excitations. The inter-dot interaction is involved only through a
single interaction parameter. The relative coordinates of individual dots form
decoupled subsystems giving rise to intra-dot excitations. As an example, the
latter are calculated exactly for two-electron dots.
Emphasis is layed on qualitative effects like: i) Influence of the magnetic
field on the lattice instability due to inter-dot interaction, ii) Closing of
the gap between the lower and the upper c.m. mode at B=0 for elliptical dots
due to dot interaction, and iii) Kinks in the single dot excitation energies
(versus magnetic field) due to change of ground state angular momentum. It is
shown that for obtaining striking qualitative effects one should go beyond
simple cubic lattices with spherical dots. We also prove a more general version
of the Kohn Theorem for quantum dot lattices. It is shown that for observing
effects of electron- electron interaction between the dots in FIR spectra
(breaking Kohn's Theorem) one has to consider dot lattices with at least two
dot species with different confinement tensors.Comment: 11 figures included as ps-file
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.
Many-body nodal hypersurface and domain averages for correlated wave functions
We outline the basic notions of nodal hypersurface and domain averages for
antisymmetric wave functions. We illustrate their properties and analyze the
results for a few electron explicitly solvable cases and discuss possible
further developments
Two Electrons in a Quantum Dot: A Unified Approach
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.Comment: 14 page
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
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
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