1 / 55

Kondo Effect in Quantum Point Contacts and Quantum Dots

Kondo Effect in Quantum Point Contacts and Quantum Dots. Yigal Meir. Department of Physics & The Ilse Katz Center for Meso- and Nano-scale Science and Technology. Outline. Quantum point contacts. Conductance quantization. Van wees et al. (1988) Wharam et al. (1988) :. Landauer formula:.

teness
Download Presentation

Kondo Effect in Quantum Point Contacts and Quantum Dots

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. Kondo Effect in Quantum Point Contacts and Quantum Dots Yigal Meir Department of Physics & The Ilse Katz Center for Meso- and Nano-scale Science and Technology

  2. Outline

  3. Quantum point contacts

  4. Conductance quantization Van wees et al. (1988) Wharam et al. (1988) :

  5. Landauer formula:

  6. Landauer Formula T eV When there are several channels:

  7. Seeing the different modes (Topinka et al. 2000/1)

  8. When there are several channels: PRL (1995) Noise: A binomial process, probability T to be transmitted, 1-T to be reflected.

  9. The 0.7 anomaly Thomas et al. (1996,1998,2000)

  10. magnetic field dependence Thomas et al. (1996)

  11. smooth barrier: sharp barrier Transmission through a barrier:

  12. Spin-density functional theory of a QPC: Formation of local moment

  13. Quantum point contact: e0+U e0 Quantum dot: e0+U e0

  14. Quantum dots e0+U e0

  15. B Semi-classically: N~50-100 Tunneling through a quantum dot: Coulomb blockade

  16. Quantum mechanical model described quantitatively by an Anderson model. Kondo effects ?

  17. A peak in the density of states at the Fermi energy Kondo Effect in Metals

  18. e0+U e0 Density of states (spectral function)

  19. Density of states: m

  20. conductance • Enhanced conductance in a Coulomb blockaded valley • Temperature scale determined by the Kondo temperature TK (exponential in coupling and energy) • Zero temperature limit of the conductance 2e2/h • Crossover function known accurately • Zero-bias anomaly as a function of voltage bias • Anomaly split by magnetic field e0 e0+U chemical potential

  21. Zero-bias anomaly that splits in finite magnetic fields by 2gB finite bias and magnetic fields

  22. Goldhaber-Gordon, Kastner (1998) Cronenwett et al. (1998)

  23. Schmidt et al. (1999)

  24. Unitarity limit in quantum dots (Delft)

  25. Quantum dots vs magnetic impurities • fully tunable, but parameters unknown • the full crossover between the Kondo limit, the mixed valence regime and the non-Kondo limit (comparison to NRG) • Kondo effect out of equilibrium • the unitarity limit • the enhancement of the Kondo effect by a magnetic field • the phase of the transmission coefficient • Kondo effect in the quantum Hall regime • absence of even-odd parity • magnetic field induced Kondo effect (singlet-triplet degeneracy) • Kondo effect due to excited states • two-impurities • the Kondo effect under external irradiation • multi-channel Kondo effect ? • noise in the Kondo regime • how long does it take ? • Kondo cloud

  26. Kondo scaling Temperature [K]

  27. (C. Marcus et al.) • zero-bias anomaly Is the 0.7 anomaly related to the Kondo effect ?

  28. temperature dependence

  29. peak width vs. Kondo temperature

  30. splitting of the zero bias anomaly with magnetic field

  31. The observation of a Kondo effect establishes the formation of a local moment in QPCs • What is different in QPCs compared to QDs ? • Large background conductance at high temperatures, • G ~ 0.5 (2e2/h) • Zero bias anomaly for small conductances

  32. V(2) V(1) V(1)V(2) The model e0+U e0 single-impurity Anderson model

  33. Kondo DOS G1 G2 e0+U e0 conductance e0 e0+U

  34. The background conductance is dominated by 01 fluctuations (G1) The Kondo effect dominated by 12 fluctuations (G2) “coexistence” of Kondo and mixed-valence Regimes !

  35. Theory (different temperatures) data Perturbation theory (following Appelbaum, 1967)

  36. Theory different magnetic fields

  37. Theory: equally spaced gate voltages Vdc

  38. Theory: zero bias anomaly splits in a finite magnetic field Vdc different gate voltages

  39. changing the depth of the level (theory): changing back-gate voltage (data): Thomas et al. Nuttinck et al.

  40. (1) (2) (1) (2) e0 different chemical potentials H Spin - current

  41. T1~ 0.5 Vg2 Vg1 observing the bound state: T1~ 0.5 Vg1 Vg2 keep Vg1 constant such that T1~ 0.5. scan Vg2 (aroundT2~ 0) – when thebound state gets occupied, T2 should jump. Sprinzak et al.: Probing bound states in quantum dots Detector signal Also Molenkamp et al. (1995)

  42. T=4.2K Observation of the bound state ?Morimoto et al. (2003)

  43. Tunneling through the bound state Preliminary results (Luescher and Goldhaber-Gordon) Peak observed in all 4 devices. No peaks at higher steps.

  44. Noise

  45. Noise measurements in QPCs[Kim et al., 2003] Also Rosch et al. (2004)

  46. Experiment (Saclay + Cambridge) Fano factor: S/I Conductance (e2/h)

  47. Induced dephasing(Heiblum, 2003)

  48. speculation – relation to dephasing in semiconductors ? Huibers et al.

More Related