Mirages and many-body effects in quantum corrals

In an experiment on quantum mirages, confinement of surface states in an elliptical corral has been used to project the Kondo effect from one focus where a magnetic impurity was placed to the other, empty, focus. The signature of the Kondo effect is seen as a Fano antiresonance in scanning tunnelling spectroscopy. This experiment combines the many-body physics of the Kondo effect with the subtle effects of confinement. In this work we review the essential physics of the quantum mirage experiment, and present new calculations involving other geometries and more than one impurity in the corral, which should be relevant for other experiments that are being made, and to discern the relative importance of the hybridization of the impurity with surface (V-s) and bulk (V-b) states. The intensity of the mirage imposes a lower bound on V-s/V-b which we estimate. Our emphasis is on the main physical ingredients of the phenomenon and the many-body aspects, like the dependence of the observed differential conductance on the geometry, which cannot be calculated with alternative one-body theories. The system is described with an Anderson impurity model solved using complementary approaches: theory of perturbation in the Coulomb repulsion U, slave bosons in the mean field and exact diagonalization plus embedding.