1. Quantum conductance and indirect exchange interaction (RKKY interaction)
Conductance of nano-systems with interactions coupled
via conduction electrons: Effect of indirect exchange interactions
cond-mat/ to appear in Eur. Phys. J. B
Yoichi Asada (Tokyo Institute of Technology)
Axel Freyn (SPEC), JLP (SPEC).
Interacting electron systems between Fermi leads:
Effective one-body transmission and correlation clouds
Rafael Molina, Dietmar Weinmann, JLP
Eur. Phys. J. B 48, 243 (2005)

2. Scattering approach to quantum transport
1. Nano-system inside which the electrons do not interact
Contact (Fermi) S
Contact (Fermi)
One body scatterer
Carbon nanotube
Molecule,
Break junction
Quantum dot of high rs
Quantum point contact g<1
YBaCuO…
2. Nano-system inside which the electrons do interact
effective one body scatterer
Fermi
S(U)
Fermi
Many body
scatterer
Value of ?
Size of the effective one body scatterer?
Relation with Kondo problem

3. How can we obtain the effective transmission coefficient
How can we obtain the effective transmission coefficient? The embedding method
Permanent current of a ring embedding the nanosystem
+ limit of infinite ring size
How can we obtain ?
Density Matrix Renormalization Group
Embedding + DMRG = exact numerical method.
Difficulty: Extension outside d=1

4. How can we obtain the size of the effective one body scatterer
How can we obtain the size of the effective one body scatterer? 2 scatterers in series
Are there corrections to the combination law of one body scatterers in series? Yes
This phenomenon is reminiscent of the RKKY interaction between magnetic moments.

5. Combination law for 2 one body scatterers in series

6. Half-filling: Even-odd oscillations + correction

7. The correction disappears when the length of the coupling lead increases with a power law

8. Magnitude of the correction
U=2 (Luttinger liquid – Mott insulator)

9. RKKY interaction (S=spin of a magnetic ion or nuclear spin)
Zener (1947)
Frohlich-Nabarro (1940)
Kasuya(1956)
Yosida(1957)
Ruderman-Kittel(1954)
Van Vleck(1962)
Friedel-Blandin(1956)

10. SPINS: Nano-systems with many body effects:
The two problems are related: Electon-electron interactions (many body effects) are necessary. The spins are not
SPINS:
Nano-systems with many body effects:

11. Spinless fermions in an infinite chain with repulsion between two central sites.
(if half-filling)
Mean field theory: Hartree-Fock approximation

12. Reminder of Hartree-Fock approximation The effect of the positive compensating potential cancels the Hartree term. Only the exchange term remains

13. Hartree-Fock approximation for a 1d tight binding model

14. 1 nanosystem inside the chain

15. Hartree-Fock describes rather well a very short nanosystem
DMRG
Hartree-Fock

16. 2 nanosystems in series

17. The results can be simplified at half-filling in the limit
1/Lc correction with even-odd oscillations characteristic of half filling.

18. Conductance of 2 nanosystems in series

19. Conductance for 2 scatterers

20. Hartree-Fock reproduces the exact results (embedding method, DMRG + extrapolation) when U<t
Correction
DMRG
Hartree-Fock

21. Role of the temperature
The effect disappears when

22. How to detect the interaction enhanced non locality of the conductance
How to detect the interaction enhanced non locality of the conductance ? (Remember Wasburn et al) U

23. Ring-Dot system with tunable coupling (K
Ring-Dot system with tunable coupling (K. Ensslin et al, cond-mat/ )