Mirages and many-body effects in quantum corrals

Abstract

In an experiment on quantum mirages, confinement of surface states in an elliptical corralhas been used to project the Kondo effect from one focus where a magnetic impurity wasplaced to the other, empty, focus. The signature of the Kondo effect is seen as a Fanoantiresonance in scanning tunnelling spectroscopy. This experiment combines themany-body physics of the Kondo effect with the subtle effects of confinement. In this workwe review the essential physics of the quantum mirage experiment, and presentnew calculations involving other geometries and more than one impurity in thecorral, which should be relevant for other experiments that are being made, and todiscern the relative importance of the hybridization of the impurity with surface(Vs) andbulk (Vb) states. The intensity of the mirage imposes a lower bound onVs/Vb which we estimate. Our emphasis is on the main physical ingredients of the phenomenonand the many-body aspects, like the dependence of the observed differentialconductance on the geometry, which cannot be calculated with alternative one-bodytheories. The system is described with an Anderson impurity model solved usingcomplementary approaches: theory of perturbation in the Coulomb repulsionU, slave bosons in the mean field and exact diagonalization plus embedding.