Mirages and many-body effects in quantum corrals

Abstract

In the experiment of the quantum mirage, 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 tunneling 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 to 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 with geometry, which cannot be calculated with alternative one-body theories. The system is described with an Anderson impurity model solved using complementary approaches: perturbation theory in the Coulomb repulsion U , slave bosons in mean field and exact 1 diagonalization plus embedding.

Spectral evolution of the SU(4) Kondo effect from the single impurity to the two-dimensional limit

“…These values are similar to those that provide a good fit of the observed line shape for a Co impurity on Cu(111) [33]. The energy of the molecular states (in the hole representation) E h was taken near to -0.1 eV, according to ab-initio calculations which find spectral density of Fe 3d xz and 3d yz states 0.1 eV above the Fermi energy [13].…”

“…dI/dV is directly proportional to the density of a mixed operator, which contains information of the conduction electrons and the localized electrons weghted by its hopping to the tip of the STM [33]:…”

“…Assuming the limit of strong repulsion U → ∞, we can neglect configurations with two or more holes in a molecular orbital, and consider only local charge fluctuations between the subspaces with n = 0, 1 holes. This limit can be implemented in the slaveboson representation [32] In STM experiments, the relevant observable is the differential conductance dI/dV , which in the limit of weak tunneling coupling between the STM tip and the system becomes proportional to the spectral density dI/dV ∼ ρ t (−eV ), where the minus sign is needed to pass from hole to electron representation, and t represents a mixed operator t [26,33,34]. We calculate the density of t-…”

Nonequilibrium magnetotransport through a quantum dot: An interpolative perturbative approach

“…[30] Slave-boson mean-field approximations have been used successfully in the equilibrium case, [12,[31][32][33][34][35] but they rely on the minimization of the free energy, which is not at a minimum in the nonequilibrium case. Nevertheless, these approximations have been used for problems out of equilibrium.…”

“…[46][47][48][49] In the equilibrium case, the second order approximation has been used for several nanoscopic systems. [12,35,[50][51][52][53] A shortcoming of this method is that it cannot describe the exponential decrease of T K in the Kondo regime as U is increased. One way to avoid this problem is to use renormalized perturbation theory (RPT).…”