1 / 39

Theory of the Fano Effect and Quantum Mirage

Theory of the Fano Effect and Quantum Mirage. STM Spectroscopy of Magnetic Adatoms on Metallic Surfaces. Local-moment formation: The Anderson model. e d + U. V. |e d |. hybridization with conduction electrons. The Anderson model - continued. Many-body Kondo resonance. e d. E F.

kolina
Download Presentation

Theory of the Fano Effect and Quantum Mirage

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Theory of the Fano Effect andQuantum Mirage STM Spectroscopy of Magnetic Adatoms on Metallic Surfaces

  2. Local-moment formation:The Anderson model ed + U V |ed| hybridization with conduction electrons

  3. The Anderson model - continued Many-body Kondo resonance ed EF ed+U

  4. Cobalt atoms deposited onto Au(111) at 4K (400A x 400A) Madhavan et al., Science 280 (1998)

  5. STM spectroscopy on and off a Co atom Madhavan et al., Science 280 (1998)

  6. STM spectroscopy across one Co atom Madhavan et al., Science 280 (1998)

  7. Theory of STM line shape: Basic ingredients STM tip Magnetic adatom Surface states Bulk states

  8. Basic ingredients - continued STM tip - Feature-less band Surface states - Two-dimensional band Bulk states - Three-dimensional band Magnetic adatom - An Anderson impurity

  9. Full Hamiltonian: Impurity Hamiltonian:

  10. Here are the local conduction-electron degree of freedom, is the position of the impurity adatom, and is the position directly beneath the STM tip

  11. Tunneling Hamiltonian: STM tip td tb ts

  12. Tunneling Hamiltonian - continued where

  13. Tunneling current: Setting msubstrate=0 and mtip=eV, and assuming weak tunneling amplitudes where is the feature-less tip DOS is the Fermi-Dirac distribution

  14. is the effective substrate DOS: with

  15. ! The differential conductance samples

  16. Evaluating Our aim is to express r f(e ) in terms of the fully dressed impurity Green function and the impurity-free surface and bulk Green functions

  17. Evaluating - continued impurity-free contributions Contribution of scattering off impurity

  18. Line shape near resonance Consider the case where Gdhas a resonance and Gsand Gb are feature-less in the relevant energy range

  19. Line shape near resonance - continued Define Real parameters Real constant p B

  20. Line shape near resonance - continued with Fano resonance!

  21. STM spectroscopy on and off a Co atom Madhavan et al., Science 280 (1998)

  22. Co on Cu(111) Manoharan et al., Nature (2000)

  23. An empty ellipse Topograph image dI/dV map Manoharan et al., Nature (2000)

  24. Quantum Mirage Extra adatom at focus: Extra adatom away from focus: Quantum mirage No quantum mirage

  25. Quantum Mirage:Spectroscopic fingerprint

  26. Recap of the main experimental findings: 1. There is a quantum mirage when a Co atom is placed at one of the foci. 2. No mirage when the Co atom is placed away from the foci. 3. The quantum mirage oscillates with4kFa. 4. The magnitude of the mirage depends only weakly on the ellipse eccentricity.

  27. Theoretical model 1. Cu(111) surface states form a 2DEG with a Fermi energy of EF=450meV and kF-1=4.75 angstroms. 2. Free 3D conduction-electron bulk states. 3. Each Co atom is modeled by a nondegenerate Anderson impurity. Ujsaghy et al., PRL (2000) 4. Hybridization with both surface and bulk states.

  28. { Perimeter Co adatoms i=1,…,N Inner Co adatom i=0

  29. Consider an STM tip placed above the surface point dI/dV measures the local conduction-electron DOS Contribution to LDOS due to inner adatom

  30. Assumptions: 1. Neglect inter-site correlations: Distance between neighboring Co adatoms is large (about 10 angstroms). 2. Only 2D propagation:

  31. Propagator for an empty ellipse Fully dressed d propagator 2a

  32. Each Co adatom on the ellipse acts as a scatterer with a surface-to-surface T-matrix component From theory of the Kondo effect, for T<TKand close to EF t The probability for surface scattering t = 1- t

  33. Where is the free 2D propagator is an N x N matrix propagator is the surface-to-surface T-matrix at each Co site

  34. Numerical results for

  35. Theory Experiment

  36. Magnitude of the projected resonance Expand in the number of scatters: Direct path Scattering off one Co atom, G1 Scattering off several cobalt atoms – add incoherently!

  37. Using Mean distance between adjacent adatoms

  38. G0is negligible compared to G1 provided Satisfied experimentally for all 0.05<e<1. Independent of the eccentricity!

  39. Conclusions STM measurements of magnetic impurities on metallic surfaces offer a unique opportunity to study the Kondo effect. The line shapes observed for individual impurities can be understood by the Kondo-Fano effect. Detailed theory presented for the quantum mirage, which explains the 4kFa oscillations and the weak dependence on the eccentricity.

More Related