One of the main foci in our group is the study of physical properties at the limits of miniaturization. On the atomic scale, for instance, it is possible to manipulate single atoms. Alternatively, one can "build" artificial atoms by confining a few electrons in a metallic or semiconducting structure. But what can one learn by reducing the physical dimensions or the dimensionality?

When reducing, for example, the dimension from 3 to 2 of an electron gas confined in a semiconducting heterostructure, new elementary quasiparticles appear. These particles have an effective fractional charge and obey fractional statistics. They are obtained when a perpendicular magnetic field is applied to the 2D electrons, which leads to the formation of composite Fermions and to the observation of the fractional quantum Hall effect.

By reducing the dimension even further, i.e., to 1D a whole new set of phenomena appear. Because of the inherent electron-electron interactions, the electron gas can no longer be described as a Fermi gas or Fermi liquid but rather as a Luttinger liquid. One of the most fascinating properties of a Luttinger liquid is the separation of charge and spin, i.e., the charge and the spin become independent of each other.

On a more applied level, the miniaturization is of tremendous interest for the whole computational business. Reducing the dimensions to such an extent that the information is not carried anymore by a macroscopic current flow but by single electrons, leads to the computing on the nanoscale. An even more fascinating outlook is the possibility to realize a quantum computer. In this case the computational information is the quantum mechanical "state" of an electron.

In short, we are interested in the electronic properties, which emerge, when electron-electron interactions, disorder and quantum phase coherence are present in reduced dimensions and dimensionalities.