825 research outputs found
Metal-insulator transition in a two-dimensional electron system: the orbital effect of in-plane magnetic field
The conductance of an open quench-disordered two-dimensional (2D) electron
system subject to an in-plane magnetic field is calculated within the framework
of conventional Fermi liquid theory applied to actually a three-dimensional
system of spinless electrons confined to a highly anisotropic (planar)
near-surface potential well. Using the calculation method suggested in this
paper, the magnetic field piercing a finite range of infinitely long system of
carriers is treated as introducing the additional highly non-local scatterer
which separates the circuit thus modelled into three parts -- the system as
such and two perfect leads. The transverse quantization spectrum of the inner
part of the electron waveguide thus constructed can be effectively tuned by
means of the magnetic field, even though the least transverse dimension of the
waveguide is small compared to the magnetic length. The initially finite
(metallic) value of the conductance, which is attributed to the existence of
extended modes of the transverse quantization, decreases rapidly as the
magnetic field grows. This decrease is due to the mode number reduction effect
produced by the magnetic field. The closing of the last current-carrying mode,
which is slightly sensitive to the disorder level, is suggested as the origin
of the magnetic-field-driven metal-to-insulator transition widely observed in
2D systems.Comment: 19 pages, 7 eps figures, the extension of cond-mat/040613
The longitudinal conductance of mesoscopic Hall samples with arbitrary disorder and periodic modulations
We use the Kubo-Landauer formalism to compute the longitudinal (two-terminal)
conductance of a two dimensional electron system placed in a strong
perpendicular magnetic field, and subjected to periodic modulations and/or
disorder potentials. The scattering problem is recast as a set of
inhomogeneous, coupled linear equations, allowing us to find the transmission
probabilities from a finite-size system computation; the results are exact for
non-interacting electrons. Our method fully accounts for the effects of the
disorder and the periodic modulation, irrespective of their relative strength,
as long as Landau level mixing is negligible. In particular, we focus on the
interplay between the effects of the periodic modulation and those of the
disorder. This appears to be the relevant regime to understand recent
experiments [S. Melinte {\em et al}, Phys. Rev. Lett. {\bf 92}, 036802 (2004)],
and our numerical results are in qualitative agreement with these experimental
results. The numerical techniques we develop can be generalized
straightforwardly to many-terminal geometries, as well as other multi-channel
scattering problems.Comment: 13 pages, 11 figure
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
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
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
Addition Spectra of Chaotic Quantum Dots: Interplay between Interactions and Geometry
We investigate the influence of interactions and geometry on ground states of
clean chaotic quantum dots using the self-consistent Hartree-Fock method. We
find two distinct regimes of interaction strength: While capacitive energy
fluctuations follow approximately a random matrix prediction for
weak interactions, there is a crossover to a regime where is
strongly enhanced and scales roughly with interaction strength. This
enhancement is related to the rearrangement of charges into ordered states near
the dot edge. This effect is non-universal depending on dot shape and size. It
may provide additional insight into recent experiments on statistics of Coulomb
blockade peak spacings.Comment: 4 pages, final version to appear in Phys. Rev. Let
Conductance Peak Distributions in Quantum Dots at Finite Temperature: Signatures of the Charging Energy
We derive the finite temperature conductance peak distributions and
peak-to-peak correlations for quantum dots in the Coulomb blockade regime
assuming the validity of random matrix theory. The distributions are universal,
depending only on the symmetry class and the temperature measured in units of
the mean level spacing, . When the temperature is comparable to
several resonances contribute to the same conductance peak and we find
significant deviations from the previously known distributions.
In contrast to the case, these distributions show a strong
signature of the charging energy and charge quantization on the dot.Comment: 14 pages, 3 Postscript figures included, RevTex, to appear as a Rapid
Communication in Physical Review
Implementation of the quantum walk step operator in lateral quantum dots
We propose a physical implementation of the step operator of the discrete
quantum walk for an electron in a one-dimensional chain of quantum dots. The
operating principle of the step operator is based on locally enhanced Zeeman
splitting and the role of the quantum coin is played by the spin of the
electron. We calculate the probability of successful transfer of the electron
in the presence of decoherence due to quantum charge fluctuations, modeled as a
bosonic bath. We then analyze two mechanisms for creating locally enhanced
Zeeman splitting based on, respectively, locally applied electric and magnetic
fields and slanting magnetic fields. Our results imply that a success
probability of > 90% is feasible under realistic experimental conditions
Statistics of Coulomb Blockade Peak Spacings within the Hartree-Fock Approximation
We study the effect of electronic interactions on the addition spectra and on
the energy level distributions of two-dimensional quantum dots with weak
disorder using the self-consistent Hartree-Fock approximation for spinless
electrons. We show that the distribution of the conductance peak spacings is
Gaussian with large fluctuations that exceed, in agreement with experiments,
the mean level spacing of the non-interacting system. We analyze this
distribution on the basis of Koopmans' theorem. We show furthermore that the
occupied and unoccupied Hartree-Fock levels exhibit Wigner-Dyson statistics.Comment: 5 pages, 2 figures, submitted for publicatio
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
- …