388 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
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
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
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
Exchange interaction in quantum rings and wires in the Wigner-crystal limit
We present a controlled method for computing the exchange coupling in
correlated one-dimensional electron systems based on the relation between the
exchange constant and the pair-correlation function of spinless electrons. This
relation is valid in several independent asymptotic regimes, including low
electron density case, under the general condition of a strong spin-charge
separation. Explicit formulas for the exchange constant are obtained for thin
quantum rings and wires with realistic Coulomb interactions by calculating the
pair-correlation function via a many-body instanton approach. A remarkably
smooth interpolation between high and low electron density results is shown to
be possible. These results are applicable to the case of one-dimensional wires
of intermediate width as well. Our method can be easily generalized to other
interaction laws, such as the inverse distance squared one of the
Calogero-Sutherland-Moser model. We demonstrate excellent agreement with the
known exact results for the latter model and show that they are relevant for a
realistic experimental setup in which the bare Coulomb interaction is screened
by an edge of a two-dimensional electron gas.Comment: 12 pages, 5 figure
The quantized Hall conductance of a single atomic wire: A proposal based on synthetic dimensions
We propose a method by which the quantization of the Hall conductance can be
directly measured in the transport of a one-dimensional atomic gas. Our
approach builds on two main ingredients: (1) a constriction optical potential,
which generates a mesoscopic channel connected to two reservoirs, and (2) a
time-periodic modulation of the channel, specifically designed to generate
motion along an additional synthetic dimension. This fictitious dimension is
spanned by the harmonic-oscillator modes associated with the tightly-confined
channel, and hence, the corresponding "lattice sites" are intimately related to
the energy of the system. We analyze the quantum transport properties of this
hybrid two-dimensional system, highlighting the appealing features offered by
the synthetic dimension. In particular, we demonstrate how the energetic nature
of the synthetic dimension, combined with the quasi-energy spectrum of the
periodically-driven channel, allows for the direct and unambiguous observation
of the quantized Hall effect in a two-reservoir geometry. Our work illustrates
how topological properties of matter can be accessed in a minimal
one-dimensional setup, with direct and practical experimental consequences.
Proximity-induced superconductivity in Landau-quantized graphene monolayers
We consider massless Dirac fermions in a graphene monolayer in the ballistic limit, subject to both a perpendicular magnetic field B and a proximity-induced pairing gap Î. When the chemical potential is at the Dirac point, our exact solution of the Bogoliubovâde Gennes equation yields Î-independent relativistic Landau levels. Since eigenstates depend on Î, many observables nevertheless are sensitive to pairing, e.g., the local density of states or the edge state spectrum. By solving the problem with an additional in-plane electric field, we also discuss how snake states are influenced by a pairing gap
Signatures of electron correlations in the transport properties of quantum dots
The transition matrix elements between the correlated and
electron states of a quantum dot are calculated by numerical diagonalization.
They are the central ingredient for the linear and non--linear transport
properties which we compute using a rate equation. The experimentally observed
variations in the heights of the linear conductance peaks can be explained. The
knowledge of the matrix elements as well as the stationary populations of the
states allows to assign the features observed in the non--linear transport
spectroscopy to certain transition and contains valuable information about the
correlated electron states.Comment: 4 pages (revtex,27kB) + 3 figures in one file ziped and uuencoded
(postscript,33kB), to appear in Phys.Rev.B as Rapid Communicatio
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