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
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1. Nano-system inside which the electrons do not interact
One body scatterer
Many body scatterer
effective one body scatterer
Value of ?Size of the effective one body scatterer?
Relation with Kondo problem
Carbon nanotubeMolecule,Break junctionQuantum dot of high rs Quantum point contact g<1YBaCuO…
2. Nano-system inside which the electrons do interact
222
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How can we obtain the effective transmission coefficient?
The embedding method
How can we obtain ? Density Matrix Renormalization Group
Embedding + DMRG = exact numerical method.
Difficulty: Extension outside d=1
Permanent current of a ring embedding the nanosystem + limit of infinite ring size
2,UEtI Feff
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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
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Half-filling: Even-odd oscillations + correction
The correction disappears when the length of the coupling lead increases with a power law
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Correction:
Magnitude of the correction
U=2 (Luttinger liquid – Mott insulator)
RKKY interaction(S=spin of a magnetic ion or nuclear spin)
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Zener (1947)Frohlich-Nabarro (1940)Kasuya(1956)Yosida(1957)Ruderman-Kittel(1954)Van Vleck(1962)Friedel-Blandin(1956)
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.
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Mean field theory: Hartree-Fock approximation
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Reminder of Hartree-Fock approximation
The effect of the positive compensating potential cancels
the Hartree term. Only the exchange term remains
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1 nanosystem inside the chain
Hartree-Fock describes rather well a very short nanosystem
DMRG
Hartree-Fock
2 nanosystems in series
CL
The results can be simplified at half-filling in the limit
1/Lc correction with even-odd oscillations characteristic of half filling.
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Conductance of 2 nanosystems in series
Conductance for 2 scatterers
16
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Hartree-Fock reproduces the exact results (embedding method, DMRG + extrapolation)
when U<t
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Correction ),( FkUA
Role of the temperature
• The effect disappears when
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BFT
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How to detect the interaction enhanced non locality of the conductance ?
(Remember Wasburn et al)
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Ring-Dot system with tunable coupling (K. Ensslin et al, cond-mat/0602246)