424 research outputs found
Rotational levels in quantum dots
Low energy spectra of isotropic quantum dots are calculated in the regime of
low electron densities where Coulomb interaction causes strong correlations.
The earlier developed pocket state method is generalized to allow for
continuous rotations. Detailed predictions are made for dots of shallow
confinements and small particle numbers, including the occurance of spin
blockades in transport.Comment: RevTeX, 10 pages, 2 figure
Theory of momentum resolved tunneling into a short quantum wire
Motivated by recent tunneling experiments in the parallel wire geometry, we
calculate results for momentum resolved tunneling into a short one-dimensional
wire, containing a small number of electrons. We derive some general theorems
about the momentum dependence, and we carry out exact calculations for up to
N=4 electrons in the final state, for a system with screened Coulomb
interactions that models the situation of the experiments. We also investigate
the limit of large using a Luttinger-liquid type analysis. We consider the
low-density regime, where the system is close to the Wigner crystal limit, and
where the energy scale for spin excitations can be much lower than for charge
excitations, and we consider temperatures intermediate between the relevant
spin energies and charge excitations, as well as temperatures below both energy
scales.Comment: 19 pages, 13 figures, clarified text in a few points, added 1 figure,
updated reference
Massless Dirac-Weyl Fermions in a T_3 Optical Lattice
We propose an experimental setup for the observation of quasi-relativistic
massless Fermions. It is based on a T_3 optical lattice, realized by three
pairs of counter-propagating lasers, filled with fermionic cold atoms. We show
that in the long wavelength approximation the T_3 Hamiltonian generalizes the
Dirac-Weyl Hamiltonian for the honeycomb lattice, however, with a larger value
of the pseudo-spin S=1. In addition to the Dirac cones, the spectrum includes a
dispersionless branch of localized states producing a finite jump in the atomic
density. Furthermore, implications for the Landau levels are discussed.Comment: 4 pages, 3 figure
Exchange Coupling in a One-Dimensional Wigner Crystal
We consider a long quantum wire at low electron densities. In this strong
interaction regime a Wigner crystal may form, in which electrons comprise an
antiferromagnetic Heisenberg spin chain. The coupling constant J is
exponentially small, as it originates from tunneling of two neighboring
electrons through the segregating potential barrier. We study this exponential
dependence, properly accounting for the many-body effects and the finite width
of the wire.Comment: 4 pages, 3 figure
Gapped Phases of Quantum Wires
We investigate possible nontrivial phases of a two-subband quantum wire. It
is found that inter- and intra-subband interactions may drive the electron
system of the wire into a gapped state. If the nominal electron densities in
the two subbands are sufficiently close to each other, then the leading
instability is the inter-subband charge-density wave (CDW). For large density
imbalance, the interaction in the inter-subband Cooper channel may lead to a
superconducting instability. The total charge-density mode, responsible for the
conductance of an ideal wire, always remains gapless, which enforces the
two-terminal conductance to be at the universal value of 2e^2/h per occupied
subband. On the contrary, the tunneling density of states (DOS) in the bulk of
the wire acquires a hard gap, above which the DOS has a non-universal
singularity. This singularity is weaker than the square-root divergency
characteristic for non-interacting quasiparticles near a gap edge due to the
"dressing" of massive modes by a gapless total charge density mode. The DOS for
tunneling into the end of a wire in a CDW-gapped state preserves the power-law
behavior due to the frustration the edge introduces into the CDW order. This
work is related to the vast literature on coupled 1D systems, and most of all,
on two-leg Hubbard ladders. Whenever possible, we give derivations of the
important results by other authors, adopted for the context of our study.Comment: 30 pages, 6 figures, to appear in "Interactions and Transport
Properties of Lower Dimensional Systems", Lecture Notes in Physics, Springe
Impurity effects in few-electron quantum dots: Incipient Wigner molecule regime
Numerically exact path-integral Monte Carlo data are presented for
strongly interacting electrons confined in a 2D parabolic quantum dot,
including a defect to break rotational symmetry. Low densities are studied,
where an incipient Wigner molecule forms. A single impurity is found to cause
drastic effects: (1) The standard shell-filling sequence with magic numbers
, corresponding to peaks in the addition energy , is
destroyed, with a new peak at N=8, (2) spin gaps decrease,
(3) for N=8, sub-Hund's rule spin S=0 is induced, and (4) spatial ordering of
the electrons becomes rather sensitive to spin. We also comment on the recently
observed bunching phenomenon.Comment: 7 pages, 1 table, 4 figures, accepted for publication in Europhysics
Letter
Ladder approximation to spin velocities in quantum wires
The spin sector of charge-spin separated single mode quantum wires is
studied, accounting for realistic microscopic electron-electron interactions.
We utilize the ladder approximation (LA) to the interaction vertex and exploit
thermodynamic relations to obtain spin velocities. Down to not too small
carrier densities our results compare well with existing quantum Monte-Carlo
(QMC) data. Analyzing second order diagrams we identify logarithmically
divergent contributions as crucial which the LA includes but which are missed,
for example, by the self-consistent Hartree-Fock approximation. Contrary to
other approximations the LA yields a non-trivial spin conductance. Its
considerably smaller computational effort compared to numerically exact
methods, such as the QMC method, enables us to study overall dependences on
interaction parameters. We identify the short distance part of the interaction
to govern spin sector properties.Comment: 6 pages, 6 figures, to appear in Physical Review
Conductance quantization and snake states in graphene magnetic waveguides
We consider electron waveguides (quantum wires) in graphene created by
suitable inhomogeneous magnetic fields. The properties of uni-directional snake
states are discussed. For a certain magnetic field profile, two spatially
separated counter-propagating snake states are formed, leading to conductance
quantization insensitive to backscattering by impurities or irregularities of
the magnetic field.Comment: 5 pages, 4 figures, final version accepted as Rapid Comm. in PR
Spin and Charge Luttinger-Liquid Parameters of the One-Dimensional Electron Gas
Low-energy properties of the homogeneous electron gas in one dimension are
completely described by the group velocities of its charge (plasmon) and spin
collective excitations. Because of the long range of the electron-electron
interaction, the plasmon velocity is dominated by an electrostatic contribution
and can be estimated accurately. In this Letter we report on Quantum Monte
Carlo simulations which demonstrate that the spin velocity is substantially
decreased by interactions in semiconductor quantum wire realizations of the
one-dimensional electron liquid.Comment: 13 pages, figures include
Effective charge-spin models for quantum dots
It is shown that at low densities, quantum dots with few electrons may be
mapped onto effective charge-spin models for the low-energy eigenstates. This
is justified by defining a lattice model based on a many-electron pocket-state
basis in which electrons are localised near their classical ground-state
positions. The equivalence to a single-band Hubbard model is then established
leading to a charge-spin () model which for most geometries reduces to a
spin (Heisenberg) model. The method is refined to include processes which
involve cyclic rotations of a ``ring'' of neighboring electrons. This is
achieved by introducing intermediate lattice points and the importance of ring
processes relative to pair-exchange processes is investigated using high-order
degenerate perturbation theory and the WKB approximation. The energy spectra
are computed from the effective models for specific cases and compared with
exact results and other approximation methods.Comment: RevTex, 24 pages, 7 figures submitted as compressed and PostScript
file
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