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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:.

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Kondo Effect in Quantum Point Contacts and Quantum Dots

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  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.

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