586 research outputs found
Phase lapses in scattering through multi-electron quantum dots: Mean-field and few-particle regimes
We show that the observed evolution of the transmission phase through
multi-electron quantum dots with more than approximately ten electrons, which
shows a universal (i.e., independent of N) as yet unexplained behavior, is
consistent with an electrostatic model, where electron-electron interaction is
described by a mean-field approach. Moreover, we perform exact calculations for
an open 1D quantum dot and show that carrier correlations may give rise to a
non-universal (i.e., N-dependent) behavior of the transmission phase, ensuing
from Fano resonances, which is consistent with experiments with a few (N < 10)
carriers. Our results suggest that in the universal regime the coherent
transmission takes place through a single level while in the few-particle
regime the correlated scattering state is determined by the number of bound
particles.Comment: 14 pages, 3 figures, RevTex4 preprint format, to appear in Phys. Rev.
Time-dependent simulation and analytical modelling of electronic Mach-Zehnder interferometry with edge-states wave packets
We compute the exact single-particle time-resolved dynamics of electronic
Mach-Zehnder interferometers based on Landau edge-states transport, and assess
the effect of the spatial localization of carriers on the interference pattern.
The exact carrier dynamics is obtained by solving numerically the
time-dependent Schroedinger equation with a suitable 2D potential profile
reproducing the interferometer design. An external magnetic field, driving the
system to the quantum Hall regime with filling factor one, is included. The
injected carriers are represented by a superposition of edge states and their
interference pattern reproduces the results of Y.Ji et al.[Nature 422, 415
(2003)]. By tuning the system towards different regimes, we find two additional
features in the transmission spectra, both related to carrier localization,
namely a damping of the Aharonov-Bohm oscillations with increasing difference
in the arms length, and an increased mean transmission that we trace to the
energy-dependent transmittance of quantum point contacts. Finally, we present
an analytical model, also accounting for the finite spatial dispersion of the
carriers, able to reproduce the above effects.Comment: two-columns, 12 pages, 9 figures; added 10 refs.; main text modified;
corrected few typos; added 3 figures of Supplementary Dat
Landau levels, edge states and magneto-conductance in GaAs/AlGaAs core-shell nanowires
Magnetic states of the electron gas confined in modulation-doped core-shell
nanowires are calculated for a transverse field of arbitrary strength and
orientation. Magneto-conductance is predicted within the Landauer approach. The
modeling takes fully into account the radial material modulation, the prismatic
symmetry and the doping profile of realistic GaAs/AlGaAs devices within an
envelope-function approach, and electron-electron interaction is included in a
mean-field self-consistent approach. Calculations show that in the low
free-carrier density regime, magnetic states can be described in terms of
Landau levels and edge states, similar to planar two-dimensional electron gases
in a Hall bar. However, at higher carrier density the dominating
electron-electron interaction leads to a strongly inhomogeneous localization at
the prismatic heterointerface. This gives rise to a complex band dispersion,
with local minima at finite values of the longitudinal wave vector, and a
region of negative magneto-resistance. The predicted marked anisotropy of the
magneto-conductance with field direction is a direct probe of the inhomogeneous
electron gas localization of the conductive channel induced by the prismatic
geometry
Exact two-body quantum dynamics of an electron-hole pair in semiconductor coupled quantum wells: a time-dependent approach
We simulate the time-dependent coherent dynamics of a spatially indirect
exciton (an electron-hole pair with the two particles confined in different
layers) in a GaAs coupled quantum well system. We use a unitary wave-packet
propagation method taking into account in full the four degrees of freedom of
the two particles in a two-dimensional system, including both the long-range
Coulomb attraction and arbitrary two-dimensional electrostatic potentials
affecting the electron and/or the hole separately. The method has been
implemented for massively parallel architectures to cope with the huge
numerical problem, showing good scaling properties and allowing evolution for
tens of picoseconds. We have investigated both transient time phenomena and
asymptotic time transmission and reflection coefficients for potential profiles
consisting of i) extended barriers and wells and ii) a single-slit geometry. We
found clear signatures of the internal two-body dynamics, with transient
phenomena in the picosecond time-scale which might be revealed by optical
spectroscopy. Exact results have been compared with mean-field approaches
which, neglecting dynamical correlations by construction, turn out to be
inadequate to describe the electron-hole pair evolution in realistic
experimental conditions.Comment: 12 two-column pages + 3 supplemental material pages, 9 figures, to
appear on Phys.Rev.
Space- and time-dependent quantum dynamics of spatially indirect excitons in semiconductor heterostructures
We study the unitary propagation of a two-particle one-dimensional
Schr\"odinger equation by means of the Split-Step Fourier method, to study the
coherent evolution of a spatially indirect exciton (IX) in semiconductor
heterostructures. The mutual Coulomb interaction of the electron-hole pair and
the electrostatic potentials generated by external gates and acting on the two
particles separately are taken into account exactly in the two-particle
dynamics. As relevant examples, step/downhill and barrier/well potential
profiles are considered. The space- and time-dependent evolution during the
scattering event as well as the asymptotic time behavior are analyzed. For
typical parameters of GaAs-based devices the transmission or reflection of the
pair turns out to be a complex two-particle process, due to comparable and
competing Coulomb, electrostatic and kinetic energy scales. Depending on the
intensity and anisotropy of the scattering potentials, the quantum evolution
may result in excitation of the IX internal degrees of freedom, dissociation of
the pair, or transmission in small periodic IX wavepackets due to dwelling of
one particle in the barrier region. We discuss the occurrence of each process
in the full parameter space of the scattering potentials and the relevance of
our results for current excitronic technologies.Comment: 28 pages, 10 figures, preprint forma
Symmetries in the collective excitations of an electron gas in core-shell nanowires
We study the collective excitations and inelastic light scattering
cross-section of an electron gas confined in a GaAs/AlGaAs coaxial quantum
well. These system can be engineered in a core-multi-shell nanowire and inherit
the hexagonal symmetry of the underlying nanowire substrate. As a result, the
electron gas forms both quasi 1D channels and quasi 2D channels at the quantum
well bents and facets, respectively. Calculations are performed within the RPA
and TDDFT approaches. We derive symmetry arguments which allow to enumerate and
classify charge and spin excitations and determine whether excitations may
survive to Landau damping. We also derive inelastic light scattering selection
rules for different scattering geometries. Computational issues stemming from
the need to use a symmetry compliant grid are also investigated systematically
Entanglement creation in semiconductor quantum dot charge qubit
We study theoretically the appearance of quantum correlations in two- and
three-electron scattering in single and double dots. The key role played by
transport resonances into entanglement formation between the single-particle
states is shown. Both reflected and transmitted components of the scattered
particle wavefunction are used to evaluate the quantum correlations between the
incident carrier and the bound particle(s) in the dots. Our investigation
provides a guideline for the analysis of decoherence effects due to the Coulomb
scattering in semiconductor quantum dots structures.Comment: 8 pages, 5 figures, Proceedings of Quantum 2010:24-28, May, 2010
Torin
Promoting creative insubordination using Escape Games in mathematics
While the development of creativity, or creative thinking, in mathematics
is considered important by many researchers, there are several
difficulties in implementing creative tasks, especially before secondary
school. Within the original context of a mathematical escape
game, this paper reports two episodes exemplifying the difficulties
met by sixth graders in abandoning stereotyped habits and acting
with creative insubordination. While in the first episode, the puzzling
task does not suffice to prompt creativity, in the second episode we
show that an original solution may prompt unexpected mathematical
contents. In conclusion, escape games could be useful to prompt
creativity even in lower grades than it is now shown in the literature,
but attention should be paid to the teacher’s role in sustaining such
creative activities
Effect of the Coulomb interaction on the electron relaxation of weakly-confined quantum dot systems
We study acoustic-phonon-induced relaxation of charge excitations in single
and tunnel-coupled quantum dots containing few confined interacting electrons.
The Full Configuration Interaction approach is used to account for the
electron-electron repulsion. Electron-phonon interaction is accounted for
through both deformation potential and piezoelectric field mechanisms. We show
that electronic correlations generally reduce intradot and interdot transition
rates with respect to corresponding single-electron transitions, but this
effect is lessened by external magnetic fields. On the other hand,
piezoelectric field scattering is found to become the dominant relaxation
mechanism as the number of confined electrons increases. Previous proposals to
strongly suppress electron-phonon coupling in properly designed single-electron
quantum dots are shown to hold also in multi-electron devices. Our results
indicate that few-electron orbital degrees of freedom are more stable than
single-electron ones.Comment: 20 pages (preprint format), 7 figures, submitted to Phys. Rev.
Magneto-photoluminescence in GaAs/AlAs core-multishell nanowires: a theoretical investigation
The magneto-photoluminescence in modulation doped core-multishell nanowires
is predicted as a function of photo-excitation intensity in non-perturbative
transverse magnetic fields. We use a self-consistent field approach within the
effective mass approximation to determine the photoexcited electron and hole
populations, including the complex composition and anisotropic geometry of the
nano-material. The evolution of the photoluminescence is analyzed as a function
of i) photo-excitation power, ii) magnetic field intensity, iii) type of
doping, and iv) anisotropy with respect to field orientation.Comment: 11 pages, 11 figures, accepted for publication in Physical Review
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