45 research outputs found
Power-law dependence of the angular momentum transition fields in few-electron quantum dots
We show that the critical magnetic fields at which a few-electron quantum dot
undergoes transitions between successive values of its angular momentum (M),
for large M values follow a very simple power-law dependence on the effective
inter-electron interaction strength. We obtain this power law analytically from
a quasi-classical treatment and demonstrate its nearly-universal validity by
comparison with the results of exact diagonalization.Comment: Uses RevTeX4, 6 figures included in the tex
Correlation between electrons and vortices in quantum dots
Exact many-body wave functions for quantum dots containing up to four
interacting electrons are computed and we investigated the distribution of the
wave function nodes, also called vortices. For this purpose, we evaluate the
reduced wave function by fixing the positions of all but one electron and
determine the locations of its zeros. We find that the zeros are strongly
correlated with respect to each other and with respect to the position of the
electrons and formulate rules describing their distribution. No multiple zeros
are found, i.e. vortices with vorticity larger than one. Our exact calculations
are compared to results extracted from the recently proposed rotating electron
molecule (REM) wave functions
Accuracy of the Hartree-Fock method for Wigner molecules at high magnetic fields
Few-electron systems confined in two-dimensional parabolic quantum dots at
high magnetic fields are studied by the Hartree-Fock (HF) and exact
diagonalization methods. A generalized multicenter Gaussian basis is proposed
in the HF method. A comparison of the HF and exact results allows us to discuss
the relevance of the symmetry of the charge density distribution for the
accuracy of the HF method. It is shown that the energy estimates obtained with
the broken-symmetry HF wave functions become exact in the infinite
magnetic-field limit. In this limit the charge density of the broken-symmetry
solution can be identified with the classical charge distribution.Comment: to appear in EPJ
Configurational entropy of Wigner crystals
We present a theoretical study of classical Wigner crystals in two- and
three-dimensional isotropic parabolic traps aiming at understanding and
quantifying the configurational uncertainty due to the presence of multiple
stable configurations. Strongly interacting systems of classical charged
particles confined in traps are known to form regular structures. The number of
distinct arrangements grows very rapidly with the number of particles, many of
these arrangements have quite low occurrence probabilities and often the
lowest-energy structure is not the most probable one. We perform numerical
simulations on systems containing up to 100 particles interacting through
Coulomb and Yukawa forces, and show that the total number of metastable
configurations is not a well defined and representative quantity. Instead, we
propose to rely on the configurational entropy as a robust and objective
measure of uncertainty. The configurational entropy can be understood as the
logarithm of the effective number of states; it is insensitive to the presence
of overlooked low-probability states and can be reliably determined even within
a limited time of a simulation or an experiment.Comment: 12 pages, 8 figures. This is an author-created, un-copyedited version
of an article accepted for publication in J. Phys.: Condens. Matter. IOP
Publishing Ltd is not responsible for any errors or omissions in this version
of the manuscript or any version derived from it. The definitive
publisher-authenticated version is available online at
10.1088/0953-8984/23/7/075302.
Topological defect motifs in two-dimensional Coulomb clusters
The most energetically favourable arrangement of low-density electrons in an
infinite two-dimensional plane is the ordered triangular Wigner lattice.
However, in most instances of contemporary interest one deals instead with
finite clusters of strongly interacting particles localized in potential traps,
for example, in complex plasmas. In the current contribution we study
distribution of topological defects in two-dimensional Coulomb clusters with
parabolic lateral confinement. The minima hopping algorithm based on molecular
dynamics is used to efficiently locate the ground- and low-energy metastable
states, and their structure is analyzed by means of the Delaunay triangulation.
The size, structure and distribution of geometry-induced lattice imperfections
strongly depends on the system size and the energetic state. Besides isolated
disclinations and dislocations, classification of defect motifs includes defect
compounds --- grain boundaries, rosette defects, vacancies and interstitial
particles. Proliferation of defects in metastable configurations destroys the
orientational order of the Wigner lattice.Comment: 14 pages, 8 figures. This is an author-created, un-copyedited version
of an article accepted for publication in J. Phys.: Condens. Matter. IOP
Publishing Ltd is not responsible for any errors or omissions in this version
of the manuscript or any version derived from it. The definitive
publisher-authenticated version is available online at
10.1088/0953-8984/23/38/38530
Currents in a many-particle parabolic quantum dot under a strong magnetic field
Currents in a few-electron parabolic quantum dot placed into a perpendicular
magnetic field are considered. We show that traditional ways of investigating
the Wigner crystallization by studying the charge density correlation function
can be supplemented by the examination of the density-current correlator.
However, care must be exercised when constructing the correct projection of the
multi-dimensional wave function space. The interplay between the magnetic field
and Euler-liquid-like behavior of the electron liquid gives rise to persistent
and local currents in quantum dots. We demonstrate these phenomena by collating
a quasi-classical theory valid in high magnetic fields and an exact numerical
solution of the many-body problem.Comment: Uses RevTeX4, figures included in the tex
Measuring topology in a laser-coupled honeycomb lattice: From Chern insulators to topological semi-metals
Ultracold fermions trapped in a honeycomb optical lattice constitute a
versatile setup to experimentally realize the Haldane model [Phys. Rev. Lett.
61, 2015 (1988)]. In this system, a non-uniform synthetic magnetic flux can be
engineered through laser-induced methods, explicitly breaking time-reversal
symmetry. This potentially opens a bulk gap in the energy spectrum, which is
associated with a non-trivial topological order, i.e., a non-zero Chern number.
In this work, we consider the possibility of producing and identifying such a
robust Chern insulator in the laser-coupled honeycomb lattice. We explore a
large parameter space spanned by experimentally controllable parameters and
obtain a variety of phase diagrams, clearly identifying the accessible
topologically non-trivial regimes. We discuss the signatures of Chern
insulators in cold-atom systems, considering available detection methods. We
also highlight the existence of topological semi-metals in this system, which
are gapless phases characterized by non-zero winding numbers, not present in
Haldane's original model.Comment: 30 pages, 12 figures, 4 Appendice
The two electron artificial molecule
Exact results for the classical and quantum system of two vertically coupled
two-dimensional single electron quantum dots are obtained as a function of the
interatomic distance (d) and with perpendicular magnetic field. The classical
system exhibits a second order structural transition as a function of d which
is smeared out and shifted to lower d values in the quantum case. The
spin-singlet - spin-triplet oscillations are shifted to larger magnetic fields
with increasing d and are quenched for a sufficiently large interatomic
distance.Comment: 4 pages, 4 ps figure