Research activities for August 2002 through June 2003 at the
National Center for Theoretical Sciences, HsinChu Taiwan
During my stay at the National Center for Theoretical Sciences
I have worked on 3 projects with Prof. Chi-Shung Tang, all concerning
electron dynamics in nanoscale semiconductor systems.
Science Institute, University of Iceland,
Dunhaga 3, IS-107 Reykjavik, Iceland
As a basis for the first two projects we designed a numerical model
of a two-dimensional electron gas (2DEG) with or without an external
magnetic field. The 2DEG is confined by a general confinement
potential that does allow us to consider quantum rings, dots
with various geometries, or short quantum wires. The numerical
model is implemented using a grid-free approach to DFT theory to
describe the Coulomb interaction between several electrons
. The use of a functional basis instead of a
spatial grid results in compact matrices which are ideal for
a parallel calculation where the construction of the CPU-intensive
elements is distributed between the nodes of a cluster.
In addition to the evaluation of the ground state properties we
extended the model to follow the time evolution of a system after
an initial short radiation pulse in the Tera-Hertz regime
is used to excite it. The direct integration of the
time evolution operator for the system within a grid-free DFT formalism
allows us to subject it to strong external perturbation and
observe nonlinear effects.
The first project centered on the effects of a short Tera-Hertz
pulse on the persistent current in a 2DEG in a quantum ring.
The results have already been published as a rapid communication
in Physical Review B . We found that
the initial perturbation can generate nonadiabatically persistent
currents in the system that may even be of opposite direction to the
original equilibrium current.
The electron density in a quantum ring with 12 electrons,
and the induced density in the same system at some later point in
time after the initial excitation.
In this finite width quantum ring the Tera-Hertz excitation
changes the state of the system by inducing a large radial
collective oscillation, a magnetoplasmon that due to the Lorentz
force maintains an angular current with a nonvanishing DC component.
We have recently compared the exciation of the collective mode
in the finite width quantum ring to what happens in a 1D
This work of ours has already been cited as displaying an example of
radiation induced phenomena that are now under intense
investigation by several groups working on the quantum Hall effect
in 2DEG's .
The time-dependent magnetization of a 2DEG in a quantum ring.
The initial excitation with duration of 3 ps
has reversed the direction of the
The second project did focus on the effects of an impurity on the
FIR-spectroscopy of a short quantum wire.
The results have been sent for publication in Physical Review B,
and are already on the arXiv preprint server .
Here we found that effects of the impurity do depend on the strength and
the polarization of the excitation. Increased excitation strength does
redshift the resonances linked with collective oscillations of
impurity states. Interestingly, we also observe a
spin-density oscillation with a much longer switch-on time than the
collective charge oscillations. The occurance of the collective
spin oscillation can be subdued by a still stronger excitation.
The ground state electron density of a short quantum wire
with and without an impurity. The center left figure shows the
effective density around the impurity in the middle of the
system. The right figure shows the magnetoplasmon in the
system after an excitation of the system with a Tera-Hertz
The third project is a long-term project with the aim to describe
a transport through the time-dependent nanosystem. We have already
taken the first steps to investigate a transport through a quantum
wire in a magnetic field. In the middle of the wire is a simple scattering
potential, that will later be replaced by the potential of
the nanosystem of interest, while the wire plays the role of the contacts.
We are now building the description of the static scattering using the
Lippmann-Schwinger equation together with the Greens function of
the wire in the magnetic field. There are still several steps that we
have to formulate carefully in the problem. Most likely we will also
allow this model and research to branch off in several directions reflecting
our interests and connection to interesting experiments.
A parabolic quantum wire with a scattering potential in the middle.
Generally, the time at the NCTS has been very valuable to me. I have
had the time to explore a new formalism with respect to a grid-free
implementation of DFT-theory and apply it to a confined 2DEG under
strong time dependent excitation. I have had time to learn FORTRAN 95,
and most important of all, I have had very good discussions and
cooperation with Prof. Chi-Shung Tang on interesting new physical
The office staff of the center has been extremely helpful
to the whole family in organizing
our environment to perfection, and we are deeply touched by the open
Taiwanese culture that has accepted us wherever we have ventured during
these 11 excellent months we will never forget.