Mesoscopic systems

A mesoscopic systems possesses at least one typical length scale (e.g. the width of a wire) much larger than a single atom but small enough to show quantum effects. Such systems are of fundamental interest as they are located at the crossover from the quantum world of atomic and molecular systems to systems described by classical physics. Studying mesoscopic systems may provide insight to questions, e.g. how does the crossover from quantum to classical take place, when do we observe quantum chaos or why don't we observe quantum fluctuations or entanglement in macroscopic systems?
The rapid development of fabrication techniques for microelectronic devices allows to design mesoscopic systems with large experimental flexibility. At the same time, the ongoing size-reduction of electronic devices in technical application implies the necessity to include quantum effects into the simulation of future electronics. It would be eligible using quantum mechanical effects to achieve an improved electronic design.

Quantum transport in two-dimensional systems

In this project we focus on so called two-dimensional electronic systems, closely related to experimental setups: At the interface of a semiconductor heterostructure electrons are confined to two-dimensional motion forming a so called two-dimensional electron gas (2DEG). Using electrostatic gates on the surface of the heterostructure, it is possible to confine the 2DEG within almost arbitrarily shaped 2D structures like wires, systems of cavities, etc. At low temperatures, conductance band electrons in these systems can possess large phase-coherence lengths, i.e. the electronic motion is governed by interference due to the boundaries. Such systems are one possible realization of matter wave billiards.
The most relevant and easiest accessible parameter of electronic devices is their conductance. We calculate the conductance on the basis of the Landauer formalism, that imposes directly the quantum mechanical probability for one electron to transmit through the device - from one terminal to another. These transmission probabilities are obtained within the Greens function formalism, which has the advantage to allow an exact description of the systems open boundaries. Even for two-dimensional systems of independent electrons the solution can numerically be challenging. In our group in cooperation with the Interdisciplinary Center for Scientific Computing a parallel version of the recursive Greens function method has been developed, that allows to investigate large systems. We are especially interested in:

• coherent control of currents via external electric and magnetic fields
• stability of transmission with regard to impurity potentials
• nonlinear conductance
• effects of inelastic scattering
• connections between quantum transport and classical mechanics

Literature

P. S. Drouvelis, P. Schmelcher and P. Bastian:
Parallel implementation of the recursive Green's function method
Journal of Computational Physics 215 (2006) 741-756