## ABSTRACT

Quantum corrals are interesting examples of solid systems nanostructured in two dimensions, not only because in the semi-classical limit they can be associated with classical orbits of particles bouncing oﬀ confining walls giving in turn rise even to chaotic motions [1], but also since they can be considered as systems with only "rim" magnetic atoms. Experimentally single quantum corrals with about 50 - 100 magnetic atoms were already detected with the first generation of spin-polarized STM techniques; see e.g. Ref. [2]. Since quantum corrals were for a few years, so to say, the "show pieces" of nanoscience, they have to be mentioned in here at least shortly. Fig. 14.1 shows the geometrical outlay of 48 Fe atoms on Cu(111) forming a

corral with a diameter of 28 a, where a is the two-dimensional lattice constant of the fcc(111) Cu surface. It was found that the circular quantum well model, discussed in detail in Ref. [3], fitted rather well with the peaks in the density of states at the central site of the corral, see Fig. 14.2, a result that per se was essentially of theoretical interest. Following the spatial distribution of the density of states at the energy corresponding to the fifth peak in Fig. 14.2, however, gave a surprisingly illustrative image of the radial oscillations with respect to an increasing distance from the center. This particular view almost looks like an experimental STM image, in particular since the chosen energy E −EF ' 0.01 Ryd refers to slightly excited electronic states.