1. Conductance of nanosystems with interaction
Anton Ramšak and Tomaž Rejec
Faculty of Mathematics and Physics, University of Ljubljana, Slovenia
Jožef Stefan Institute, Ljubljana, Slovenia
QinetiQ, Great Malvern, UK

2. Strong correlations in nanosystemsJ V

3. Open system

4. Open system Ring with auxiliary flux1 N
Time-reversal symmetry: f0 = 0

5. Number of electrons odd
Fermi liquid universality of the ground-state energy
Number of electrons odd

6. Linear conductance from the ground-state energy

7. Linear conductance from the ground-state energy

8. Linear conductance from the ground-state energy

9. Example I: Non-interacting double-barrier system

10. Example II : Kondo effect in a quantum dot

11. Example III : Aharonov – Bohm ring
Broken time-reversal symmetry
Compared with W. Hoffstetter et al.,
Phys. Rev. Lett. 87, (2001)

12. Summary
The ground state energy of the ring system with flux has a universal form if ‘open’ system is a Fermi liquid at T = 0.
E(f)
Linear conductance can then be extracted from the ground-state energy:
T. Rejec and A. Ramšak, Phys. Rev. B 68, (2003); (2003)

13. Formulae are exact IF the system is Fermi liquid
note:
linear conductance
zero temperature
non-interacting single-channel leads

14. Conductance formalisms
Meir – Wingreen formula
non-equilibrium transport: T ≠ 0, V ≠ 0
Landauer – Büttiker formula
linear response regime: T ≠ 0, V ~ 0
Kubo formula
zero-temperature linear response: T = 0, V ~ 0
In Fermi liquid systems
Fisher – Lee relation …

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

18. Step 4. Validity of the conductance formulas