Research activities for August 2002 through June 2003 at the National Center for Theoretical Sciences, HsinChu Taiwan

Vidar Gudmundsson,

Science Institute, University of Iceland,

Dunhaga 3, IS-107 Reykjavik, Iceland

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.

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 [1]. 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.

Figure 1: 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.

The results have already been published as a rapid communication in Physical Review B [3]. 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.

Figure 2: 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 persistent current.

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 ring [4]. 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 [5].

The second project did focus on the effects of an impurity on the FIR-spectroscopy of a short quantum wire.

Figure 3: 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 radiation.

The results have been sent for publication in Physical Review B, and are already on the arXiv preprint server [2]. 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 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.

Figure 4: A parabolic quantum wire with a scattering potential in the middle.

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.

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 phenomena.

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.