752 research outputs found
Gauge invariant grid discretization of Schr\"odinger equation
Using the Wilson formulation of lattice gauge theories, a gauge invariant
grid discretization of a one-particle Hamiltonian in the presence of an
external electromagnetic field is proposed. This Hamiltonian is compared both
with that obtained by a straightforward discretization of the continuous
Hamiltonian by means of balanced difference methods, and with a tight-binding
Hamiltonian. The proposed Hamiltonian and the balanced difference one are used
to compute the energy spectrum of a charged particle in a two-dimensional
parabolic potential in the presence of a perpendicular, constant magnetic
field. With this example we point out how a "naive" discretization gives rise
to an explicit breaking of the gauge invariance and to large errors in the
computed eigenvalues and corresponding probability densities; in particular,
the error on the eigenfunctions may lead to very poor estimates of the mean
values of some relevant physical quantities on the corresponding states. On the
contrary, the proposed discretized Hamiltonian allows a reliable computation of
both the energy spectrum and the probability densities.Comment: 7 pages, 4 figures, discussion about tight-binding Hamiltonians adde
Dynamic Nuclear Polarization in Double Quantum Dots
We theoretically investigate the controlled dynamic polarization of lattice
nuclear spins in GaAs double quantum dots containing two electrons. Three
regimes of long-term dynamics are identified, including the build up of a large
difference in the Overhauser fields across the dots, the saturation of the
nuclear polarization process associated with formation of so-called "dark
states," and the elimination of the difference field. We show that in the case
of unequal dots, build up of difference fields generally accompanies the
nuclear polarization process, whereas for nearly identical dots, build up of
difference fields competes with polarization saturation in dark states. The
elimination of the difference field does not, in general, correspond to a
stable steady state of the polarization process.Comment: 4 pages, 2 figure
Rashba-control for the spin excitation of a fully spin polarized vertical quantum dot
Far infrared radiation absorption of a quantum dot with few electrons in an
orthogonal magnetic field could monitor the crossover to the fully spin
polarized state. A Rashba spin-orbit coupling can tune the energy and the spin
density of the first excited state which has a spin texture carrying one extra
unit of angular momentum. The spin orbit coupling can squeeze a flipped spin
density at the center of the dot and can increase the gap in the spectrum.Comment: 4 pages, 5 figure
Wigner Crystallization in a Quasi-3D Electronic System
When a strong magnetic field is applied perpendicularly (along z) to a sheet
confining electrons to two dimensions (x-y), highly correlated states emerge as
a result of the interplay between electron-electron interactions, confinement
and disorder. These so-called fractional quantum Hall (FQH) liquids form a
series of states which ultimately give way to a periodic electron solid that
crystallizes at high magnetic fields. This quantum phase of electrons has been
identified previously as a disorder-pinned two-dimensional Wigner crystal with
broken translational symmetry in the x-y plane. Here, we report our discovery
of a new insulating quantum phase of electrons when a very high magnetic field,
up to 45T, is applied in a geometry parallel (y-direction) to the
two-dimensional electron sheet. Our data point towards this new quantum phase
being an electron solid in a "quasi-3D" configuration induced by orbital
coupling with the parallel field
Chaos in Quantum Dots: Dynamical Modulation of Coulomb Blockade Peak Heights
The electrostatic energy of an additional electron on a conducting grain
blocks the flow of current through the grain, an effect known as the Coulomb
blockade. Current can flow only if two charge states of the grain have the same
energy; in this case the conductance has a peak. In a small grain with
quantized electron states, referred to as a quantum dot, the magnitude of the
conductance peak is directly related to the magnitude of the wavefunction near
the contacts to the dot. Since dots are generally irregular in shape, the
dynamics of the electrons is chaotic, and the characteristics of Coulomb
blockade peaks reflects those of wavefunctions in chaotic systems. Previously,
a statistical theory for the peaks was derived by assuming these wavefunctions
to be completely random. Here we show that the specific internal dynamics of
the dot, even though it is chaotic, modulates the peaks: because all systems
have short-time features, chaos is not equivalent to randomness. Semiclassical
results are derived for both chaotic and integrable dots, which are
surprisingly similar, and compared to numerical calculations. We argue that
this modulation, though unappreciated, has already been seen in experiments.Comment: 4 pages, 3 postscript figs included (2 color), uses epsf.st
The Addition Spectrum and Koopmans' Theorem for Disordered Quantum Dots
We investigate the addition spectrum of disordered quantum dots containing
spinless interacting fermions using the self-consistent Hartree-Fock
approximation. We concentrate on the regime r_s >~1, with finite dimensionless
conductance g. We find that in this approximation the peak spacing fluctuations
do not scale with the mean single particle level spacing for either Coulomb or
nearest neighbour interactions when r_s >~1. We also show that Koopmans'
approximation to the addition spectrum can lead to errors that are of order the
mean level spacing or larger, both in the mean addition spectrum peak spacings,
and in the peak spacing fluctuations.Comment: 35 pages including 22 figures (eps
Density Modulations and Addition Spectra of Interacting Electrons in Disordered Quantum Dots
We analyse the ground state of spinless fermions on a lattice in a weakly
disordered potential, interacting via a nearest neighbour interaction, by
applying the self-consistent Hartree-Fock approximation. We find that charge
density modulations emerge progressively when r_s >1, even away from
half-filling, with only short-range density correlations. Classical geometry
dependent "magic numbers" can show up in the addition spectrum which are
remarkably robust against quantum fluctuations and disorder averaging.Comment: 4 pages, 3 eps figure
Crossover from Fermi liquid to Wigner molecule behavior in quantum dots
The crossover from weak to strong correlations in parabolic quantum dots at
zero magnetic field is studied by numerically exact path-integral Monte Carlo
simulations for up to eight electrons. By the use of a multilevel blocking
algorithm, the simulations are carried out free of the fermion sign problem. We
obtain a universal crossover only governed by the density parameter . For
, the data are consistent with a Wigner molecule description, while
for , Fermi liquid behavior is recovered. The crossover value is surprisingly small.Comment: 4 pages RevTeX, 3 figures, corrected Tabl
Spin-density-functional theory of circular and elliptical quantum dots
Using spin-density-functional theory, we study the electronic states of a
two-dimensional parabolic quantum dot with up to N=58 electrons. We observe a
shell structure for the filling of the dot with electrons. Hund's rule
determines the spin configuration of the ground state, but only up to 22
electrons. At specific N, the ground state is degenerate, and a small
elliptical deformation of the external potential induces a rotational
charge-density-wave (CDW) state. Previously identified spin-density-wave (SDW)
states are shown to be artifacts of broken spin symmetry in density-functional
theory.Comment: 10 pages, 3 figure
Quantum Hall effect in single wide quantum wells
We study the quantum Hall states in the lowest Landau level for a single wide
quantum well. Due to a separation of charges to opposite sides of the well, a
single wide well can be modelled as an effective two level system. We provide
numerical evidence of the existence of a phase transition from an
incompressible to a compressible state as the electron density is increased for
specific well width. Our numerical results show a critical electron density
which depends on well width, beyond which a transition incompressible double
layer quantum Hall state to a mono-layer compressible state occurs. We also
calculate the related phase boundary corresponding to destruction of the
collective mode energy gap. We show that the effective tunneling term and the
interlayer separation are both renormalised by the strong magnetic field. We
also exploite the local density functional techniques in the presence of strong
magnetic field at to calculate renormalized . The
numerical results shows good agreement between many-body calculations and local
density functional techniques in the presence of a strong magnetic field at
. we also discuss implications of this work on the
incompressible state observed in SWQW.Comment: 30 pages, 7 figures (figures are not included
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