1. Quantum Dots – Past, Present and Open Questions Yigal Meir Department of Physics & The Ilse Katz Center for Meso- and Nano-scale Science and Technology Beer Sheva, ISRAEL

2. Quantum dot – an artificial device, small enough so that quantization of energy levels and electron charge are important

3. vertical quantum dots Single molecules

4. Tarucha et al.

5. VgVg LL RR Transmission resonance when

6. Example: 2d harmonic oscillator

8. Coulomb Blockade charging of a capacitor

9. Coulomb blockade peaks Single electron transistor Kastner et al.

10. Now include quantum effects: energies wavefunctions The peak amplitude depends on the wavefunction the electron tunnels into

11. n=1 n=0 Example - Quantum Hall effect: All states within a landau level are degenerate, except edge states, E n =(n+1/2)h  c The radii are quantized  r 2 =n  0 (n – Landau level index)

12. McEuen et al.

14. Spin flips Kouwenhoven et al.

15. Level statistics and random matrix theory

16. Artificial molecules Dynamics

17. RR LL Probes the excited states Nonlinear transport

18. Foxman et al.

19. Correlation between excited state of N electrons and the ground states of N+1 electrons Marcus et al.

20. B

21. Is transport through a quantum dot coherent ? Yacoby, Heiblum

24. Checking quantum measurement theory Aleiner, Wingreen, Meir

25. Buks et al.

26. The Kondo effect

27. Relevant to transport through quantum dots Ng and Lee Glazman and Raikh

28. chemical potential Conductance (2e 2 /h)

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

30. Kouwenhoven et al.

31. Temperature [K] Kondo scaling Goldhaber-Gordon et al.

32. The Kondo effect out of equilibrium Meir, Wingreen, Lee

33. The two-impurity Anderson model Georges & Meir chang

34. Kondo vs. RKKY Marcus et al.

35. The two-channel Kondo effect Non- Fermi liquid ground state

36. Oreg & Goldhaber-Gordon

37. More open questions Phase of transmission amplitude Heiblum

39. eV=  E Inelastic process ? Ensslin

40. Noise measurements and electron bunching Heiblum

41. Thomas et al. (1996,1998,2000) The “0.7 anomaly”

42. Rejec and Meir

43. conclusions Quantum dots are controllable miniaturized devices, which can be instrumental in our understanding of mesoscopic and strongly correlated systems. May be the basic ingredient in applications of quantum computing. In spite of their apparent simplicity, still many open questions.

44. P. A. LeeP. NordlanderM. Kastner N. S. WingreenM. PustilnikU. Meirav J. KinaretA. GolubP. McEuen B. L. AltshulerY. AvishaiE. Foxman X.-G. WenA. AuerbachD. Goldhaber-Gordon A.-P. JauhoP. RojtL. Kouwenhoven A. L. AleinerO. Entin-WohlmanR. Ashoori E. ShopenA. AharonyM. Heiblum A. GeorgesT. AonoA. Yacoby D. C. LangrethY. DubiC. Marcus K. HiroseT. RejecK. Ensslin Y. GefenT. Ihn Theory:Experiment: