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 Vs and bulk Vb states. The intensity of the mirage imposes a lower bound to Vs/Vb 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 diagonalization plus embedding.

52 pages, 16 figures, some mistakes corrected and references updated. To appear in in Journal of Physics: Condensed Matter

References in corpus (10)

• Kondo temperature of magnetic impurities at surfaces
• Spin filters with Fano dots
• Simple model for scanning tunneling spectroscopy of noble metal surfaces with adsorbed Kondo impurities
• Role of surface states in STM spectroscopy of (111) metal surfaces with Kondo adsorbates
• Detection of topological transitions by transport through molecules and nanodevices
• Transport through an interacting system connected to leads
• Spectral densities of Kondo impurities in nanoscopic systems
• Kondo resonance for orbitally degenerate systems
• STM conductance of Kondo impurities on open and structured surfaces
• Quantum corral wave function engineering

Cited by in corpus (33)

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• Zero-field Kondo splitting and quantum-critical transition in double quantum dots
• Quantum Phase Extraction in Isospectral Electronic Nanostructures
• Fano-type interference in quantum dots coupled between metallic and superconducting leads
• Nonequilibrium magnetotransport through a quantum dot: An interpolative perturbative approach
• Nonequilibrium dynamics of a singlet-triplet Anderson impurity near the quantum phase transition
• Nonequilibrium conductance of a nanodevice for small bias voltage
• Single-Atom Gating of Quantum State Superpositions
• Conductance through an array of quantum dots
• A Novel Approach to Study Highly Correlated Nanostructures: The Logarithmic Discretization Embedded Cluster Approximation
• Restriction Bounds for the Free Resolvent and Resonances in Lossy Scattering
• Nonequilibrium transport through magnetic vibrating molecules
• Spectral density of an interacting dot coupled indirectly to conducting leads
• Spatially dependent Kondo effect in Quantum Corrals
• The effective Kondo model for a trimer on a metallic surface
• Transition between SU(4) and SU(2) Kondo effect
• Theory of Scanning Tunneling Spectroscopy: from Kondo Impurities to Heavy Fermion Materials
• Electron Transport through a Molecular Conductor with Center-of-Mass Motion
• Quantifying the leading role of the surface state in the Kondo effect of Co/Ag(111)
• Spectral evolution of the SU(4) Kondo effect from the single impurity to the two-dimensional lattice
• Theory of differential conductance of Co on Cu(111) including Co s and d orbitals, and surface and bulk Cu states
• Focussing quantum states
• Valence fluctuations in a lattice of magnetic molecules: application to iron(II) phtalocyanine molecules on Au(111)
• Surface states influence in the conductance spectra of Co adsorbed on Cu(111)
• Topological quantum phase transition in individual Fe Atoms on MoS${}_2$/Au(111)
• Two-stage three-channel Kondo physics for an FePc molecule on the Au(111) surface
• Quantum correlations in nanostructured two-impurity Kondo systems
• Scanning tunneling microscopy of adsorbed molecules on metalic surfaces for nearly localized atomic states
• Spin selective transport through Aharonov-Bohm and Aharonov-Casher triple quantum dot systems
• Static and dynamical properties of elliptic quantum corrals
• Kondo temperature when the Fermi level is near a step in the conduction density of states
• Kondo effect in transport through Aharonov-Bohm and Aharonov-Casher interferometers
• Kondo physics of magnetic adatoms on metallic surfaces when the onset of the surface conduction density of states crosses the Fermi level