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/0605756 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)

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

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

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.

Combination law for 2 one body scatterers in series

Half-filling: Even-odd oscillations + correction

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

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

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)

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:

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

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

Hartree-Fock approximation for a 1d tight binding model

1 nanosystem inside the chain

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

2 nanosystems in series

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

Conductance of 2 nanosystems in series

Conductance for 2 scatterers

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

Role of the temperature The effect disappears when

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

Ring-Dot system with tunable coupling (K Ring-Dot system with tunable coupling (K. Ensslin et al, cond-mat/0602246)