2. A. Ramšak 1,2 and T. Rejec 2 1 Faculty of Mathematics and Physics, University of Ljubljana 2 J. Stefan Institute, Ljubljana, Slovenia Conductance of nano-systems with interaction

3. Nature 417, 725 - 729 (13 June 2002) Kondo resonance in a single-molecule transistor WENJIE LIANG*, MATTHEW P. SHORES†, MARC BOCKRATH*, JEFFREY R. LONG† & HONGKUN PARK*

4. open system

5. Conductance: ΔI = GΔV +ΔV

6. Conductance: ΔI = GΔV +ΔV IF the system is the Fermi liquid 

9. odd even Gogolin (1994): persistent currents for non-interacting systems

10. Conductance formulas: two-point energy: Favand and Milla (1998): for non-interacting systems, g<<1 Molina et al. (2003)

11. Conductance formulas: two-point energy: persistent current: Sushkov (2001) Meden and Schollwöck (2003)

12. Conductance formulas: two-point energy: persistent current: charge stiffness:

13. min max charge stiffness:

14. note: Fermi liquid linear conductance zero temperature non-interacting single-channel leads

15. Proof of the method Step 1. Conductance of a Fermi liquid system at T=0 Kubo T=0 define (n.i.: Fisher-Lee) ‘Landauer’

16. Step 2. Quasiparticle Hamiltonian (Landau Fermi liquid)

17. Step 3. Quasiparticles in a finite system N

18. Step 4. Quasiparticle energies ‘single (quasi)particle energy’; also eigenenergy of  Φ dependence of is as in non-interacting systems

19. Step 5. Non-interacting systems

20. open system

21. ring system

22. Step 5. Non-interacting system  ground-state energy:

23. Examples 1 Noninteracting system

24. 2 Anderson impurity model Wiegman, Tsvelick (1982)

25. 3 Double quantum dot Oguri, PRB 56, 13422 (1997)

26. broken time reversal symmetry (e.g., due to external magnetic field) : 4 Aharonov-Bohm system (Kondo-Fano)

27. broken time reversal symmetry (e.g., due to external magnetic field) : 4 Aharonov-Bohm system (Kondo-Fano)

28. Bułka, Stefanski, PRL (2001) Hofstetter, König, Schoeller, PRL (2001)

29. Summary: 1.IF the system is Fermi liquid … 2.Calculate the ground-state energy of the interacting (ring) system 3.Determine the conductance from the two (four)-point energy formula T. Rejec and A. Ramšak, PRB 68, 033306 (2003) T. Rejec and A. Ramšak, PRB 68, 035342 (2003)

31. ‘0.7 anomaly’

32. 1988

34. “0.7 structure” Thomas et al. PRL 77, 136 (1996):

36. Resonant scattering

37. Singlet transmission Triplet transmission

38. Results: “1/4” and “3/4” anomalies

39. PRB 44, 13549 (1991) exp.: “0.7” and “0.3” Phil. Mag. 77, 1213 (1998)

40. V-groove

41. PRL 2002

43. Summary “0.7” anomaly is “ 1/4 ”+” 3/4 ” anomaly anomalies also in S and  in magnetic field “1/2” extended Anderson model (Kondo) open problems: - Kondo physics? - doping dependence? - “ 0.5 ” anomaly Rejec, Ramšak, Jefferson, PRB 67, 075311 (2003) and refs. therein

45. Tomi Rejec

47. Narrow wires (10~20 nm) “V”-groove