538 research outputs found
Far-Infrared Excitations below the Kohn Mode: Internal Motion in a Quantum Dot
We have investigated the far-infrared response of quantum dots in modulation
doped GaAs heterostructures. We observe novel modes at frequencies below the
center-of-mass Kohn mode. Comparison with Hartree-RPA calculations show that
these modes arise from the flattened potential in our field-effect confined
quantum dots. They reflect pronounced relative motion of the charge density
with respect to the center-of-mass.Comment: 8 pages, LaTeX with integrated 6 PostScript figure
Collective excitations in Quantum Dot
We investigate different types of collective excitations in a quantum dot
containing finite number of electrons at zero magnetic field. To estimate the
excitation energies analytically we follow the energy weighted sum-rule
approach. We consider the most general multipole excitation with angular
momentum l, and the breathing mode excitation (monopole excitation) of a large
quantum dot, for three different types of effective electron-electron
interaction. These are the logarithmic interaction, the short range
pseudopotential and the coulomb interaction. The ground state density of the
many-body system is calculated within Thomas-Fermi approximation. The
analytical results for the collective excitation energies and their dependence
on the system size and other external parameters are discussed in detail.Comment: Tex file, 4 figures ps file
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
Magnetoplasmon excitations in arrays of circular and noncircular quantum dots
We have investigated the magnetoplasmon excitations in arrays of circular and
noncircular quantum dots within the Thomas-Fermi-Dirac-von Weizs\"acker
approximation. Deviations from the ideal collective excitations of isolated
parabolically confined electrons arise from local perturbations of the
confining potential as well as interdot Coulomb interactions. The latter are
unimportant unless the interdot separations are of the order of the size of the
dots. Local perturbations such as radial anharmonicity and noncircular symmetry
lead to clear signatures of the violation of the generalized Kohn theorem. In
particular, the reduction of the local symmetry from SO(2) to results in
a resonant coupling of different modes and an observable anticrossing behaviour
in the power absorption spectrum. Our results are in good agreement with recent
far-infrared (FIR) transmission experiments.Comment: 25 pages, 6 figures, typeset in RevTe
Magnetoplasmon excitations in an array of periodically modulated quantum wires
Motivated by the recent experiment of Hochgraefe et al., we have investigated
the magnetoplasmon excitations in a periodic array of quantum wires with a
periodic modulation along the wire direction. The equilibrium and dynamic
properties of the system are treated self-consistently within the
Thomas-Fermi-Dirac-von Weizsaecker approximation. A calculation of the
dynamical response of the system to a far-infrared radiation field reveals a
resonant anticrossing between the Kohn mode and a finite-wavevector
longitudinal excitation which is induced by the density modulation along the
wires. Our theoretical calculations are found to be in excellent agreement with
experiment.Comment: 9 pages, 8 figure
Collective charge-density excitations of non-circular quantum dots in a magnetic field
Recent photoabsorption measurements have revealed a rich fine structure in
the collective charge-density excitation spectrum of few-electron quantum dots
in the presence of magnetic fields. We have performed systematic computational
studies of the far-infrared density response of quantum dots, using
time-dependent density-functional theory in the linear regime and treating the
dots as two-dimensional disks. It turns out that the main characteristics
observed in the experiment can be understood in terms of the electronic shell
structure of the quantum dots. However, new features arise if a breaking of the
circular symmetry of the dots is allowed, leading to an improved description of
the experimental results.Comment: 18 pages, 5 figures, submitted to Phys. Rev.
Plasmon-pole approximation for semiconductor quantum wire electrons
We develop the plasmon-pole approximation for an interacting electron gas
confined in a semiconductor quantum wire. We argue that the plasmon-pole
approximation becomes a more accurate approach in quantum wire systems than in
higher dimensional systems because of severe phase-space restrictions on
particle-hole excitations in one dimension. As examples, we use the
plasmon-pole approximation to calculate the electron self-energy due to the
Coulomb interaction and the hot-electron energy relaxation rate due to
LO-phonon emission in GaAs quantum wires. We find that the plasmon-pole
approximation works extremely well as compared with more complete many-body
calculations.Comment: 16 pages, RevTex, figures included. Also available at
http://www-cmg.physics.umd.edu/~lzheng
Inelastic Coulomb scattering rates due to acoustic and optical plasmon modes in coupled quantum wires
We report a theoretical study on the inelastic Coulomb scattering rate of an
injected electron in two coupled quantum wires in quasi-one-dimensional doped
semiconductors. Two peaks appear in the scattering spectrum due to the optical
and the acoustic plasmon scattering in the system. We find that the scattering
rate due to the optical plasmon mode is similar to that in a single wire but
the acoustic plasmon scattering depends crucially on its dispersion relation at
small . Furthermore, the effects of tunneling between the two wires are
studied on the inelastic Coulomb scattering rate. We show that a weak tunneling
can strongly affect the acoustic plasmon scattering.Comment: 6 Postscript figure
Far-infrared edge modes in quantum dots
We have investigated edge modes of different multipolarity sustained by
quantum dots submitted to external magnetic fields. We present a microscopic
description based on a variational solution of the equation of motion for any
axially symmetric confining potential and multipole mode. Numerical results for
dots with different number of electrons whose ground-state is described within
a local Current Density Functional Theory are discussed. Two sum rules, which
are exact within this theory, are derived. In the limit of a large neutral dot
at B=0, we have shown that the classical hydrodynamic dispersion law for edge
waves \omega(q) \sim \sqrt{q \ln (q_0/q)} holds when quantum and finite size
effects are taken into account.Comment: We have changed some figures as well as a part of the tex
Far-infrared edge modes in quantum dots
We have investigated edge modes of different multipolarity sustained by
quantum dots submitted to external magnetic fields. We present a microscopic
description based on a variational solution of the equation of motion for any
axially symmetric confining potential and multipole mode. Numerical results for
dots with different number of electrons whose ground-state is described within
a local Current Density Functional Theory are discussed. Two sum rules, which
are exact within this theory, are derived. In the limit of a large neutral dot
at B=0, we have shown that the classical hydrodynamic dispersion law for edge
waves \omega(q) \sim \sqrt{q \ln (q_0/q)} holds when quantum and finite size
effects are taken into account.Comment: We have changed some figures as well as a part of the tex
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