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A. Ramšak* J. Mravlje T. Rejec* R. Žitko J. Bonča *

The Kondo effect in multiple quantum dot systems and deformable molecules. http://gawain.elte.hu/mcrtn/. A. Ramšak* J. Mravlje T. Rejec* R. Žitko J. Bonča *. *. Department of Physics Faculty of Mathematics and Physics University of Ljubljana. Outline. Conductance

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A. Ramšak* J. Mravlje T. Rejec* R. Žitko J. Bonča *

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  1. The Kondo effect in multiple quantum dot systems and deformable molecules http://gawain.elte.hu/mcrtn/ A. Ramšak* J. Mravlje T. Rejec* R. Žitko J. Bonča* * Department of Physics Faculty of Mathematics and Physics University of Ljubljana

  2. Outline • Conductance • Kondo in a single quantum dot • Methods • Double quantum dots • Triple quantum dots • Deformable molecules • Center-of-mass motion • Summary

  3. Conductance

  4. Conductance

  5. Non-interacting systems: U=0

  6. Non-interacting systems: U=0

  7. The Anderson model: U > 0

  8. The Kondo effect in a quantum dot

  9. The Kondo effect in a quantum dot

  10. The Kondo effect in a quantum dot

  11. The Kondo effect in a quantum dot

  12. The Kondo effect in a quantum dot

  13. The Kondo effect in a quantum dot

  14. The Kondo effect in a quantum dot

  15. The Kondo effect in a quantum dot

  16. The Kondo effect in a quantum dot

  17. The Kondo effect in a quantum dot

  18. The Kondo effect in a quantum dot

  19. The Kondo effect in a quantum dot

  20. The Kondo effect in a quantum dot

  21. The Kondo effect in a quantum dot

  22. The Kondo effect in a quantum dot

  23. The Kondo effect in a quantum dot

  24. The Kondo effect in a quantum dot

  25. The Kondo effect in a quantum dot

  26. 1 “Ring system”

  27. “Open system”

  28. “Open system”

  29. IF open system is Fermi liquid the GS energy of a large ring system is an universal function of flux T. Rejec and A. Ramšak, PRB68, 033306 (2003); 68035342 (2003)

  30. Linear conductance from the ground-state energy See also: J. Favand and F. Mila (Phys. J. 1998); O. Sushkov (PRB 2001);R. Molina et al. (PRB 2003)

  31. Linear conductance from the ground-state energy

  32. Linear conductance from the ground-state energy

  33. Aharonov – Bohm rings Broken time-reversal symmetry T. Rejec and A. Ramšak, PRB68, 033306 (2003)

  34. The Kondo effect in a quantum dot numerical tests… U=0

  35. The Kondo effect in a quantum dot: finite temperature low T U=0 high T

  36. The Kondo effect in a quantum dot: finite temperature low T high T

  37. The Kondo effect in a quantum dot: finite temperature low T high T

  38. Fingerprints of Kondo…

  39. Fingerprints of Kondo…

  40. Fingerprints of Kondo…

  41. Fingerprints of Kondo…

  42. Chan et al, Nanotechnology 15, 609 (2004) Vidan et al, Applied Phys. Lett. 85, 3602 (2004) Elzerman et al, PRB 67, 16308 (2003) QD QD Electrostatic gates Multiple quantum dot systems

  43. Double quantum dot

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