408 Progress of Theoretical Physics Supplement No. 176, 2008 Quantum Properties of Elliptical Corrals Marco Nizama and Karen Hallberg Centro At´omico Bariloche and Instituto Balseiro, 8400 Bariloche, Argentina Quantum corrals present interesting properties due to the combination of confinement and, in the case of elliptical corrals, to their focalizing properties. We analyze time-dependent properties of the bare ellipse. We also study the case when two magnetic impurities are added to the non-interacting corral, where they interact via a superexchange AF interaction J with the surface electrons in the ellipse. When both impurities are located at the foci of the system, they experience an enhanced magnetic interaction, as compared to the one they would have in an open surface. For small J they are locked in a singlet state, which weakens for larger values of this parameter. When J is much larger than the hopping parameter of the electrons in the ellipse, both spins decorrelate while forming a local singlet with the electrons of the ellipse, thus presenting a confined RKKY-Kondo transition. We can also interpret this behaviour analyzing the von Neumann entropy between the localized impurities and the itinerant electrons of the ellipse: for small J the entropy is nearly zero while for large J it is maximum. §1. Introduction Thanks to the recent advancement in the knowledge and fabrication of nanoscopic systems the observation of the phenomenon known as the quantum mirage has been possible. This effect arises in nanoscopic systems called quantum corrals, where the electron wave functions are confined to a finite region by means of a potential barrier formed by atoms encircling a closed region in space. In a fascinating experiment, Manoharan et al. 1) built elliptical corrals with Co atoms on the (111) surface of Cu. The Cu (111) surface contains a band of surface states, orthogonal to the bulk states, which can be represented as a two-dimensional electron gas confined at the surface. 3) The Fermi level is placed at 450 meV above the bottom of the surface band. The atoms forming the corral act as scattering centers which tend to confine the surface electrons inside the corral. Several authors have analyzed these experiments with one or more impurities considering different configurations (see review articles in 2),3) and 4)–17)). In Refs. 11)–13) it was suggested that two impurities located at the foci of the system will interact strongly as a consequence of the focalizing properties of quantum elliptic corrals. Such a prediction has been supported by Stepanyuk et al. 18) who reported results of first principle calculations of the exchange coupling between magnetic impurities inside quantum corrals. Several factors affect the physical properties of quantum corrals, like confine- ment, many-body effects and quantum interference. So far the main interest has been focused on the static properties of these systems while the dynamical behaviour is mostly unexplored. In Ref. 13) real-time dynamics of non-interacting corrals for different kinds of perturbations has been studied showing that the focalizing proper- ties of the system have important consequences on the physical behaviour. Here an isolated ellipse describing a closed quantum system containing an arbitrary number Downloaded from https://academic.oup.com/ptps/article-abstract/doi/10.1143/PTPS.176.408/1883938 by guest on 08 June 2020