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Quantum conductance and indirect exchange interaction (RKKY interaction)

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)

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Quantum conductance and indirect exchange interaction (RKKY interaction)

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  1. Quantum conductance and indirectexchange interaction (RKKY interaction) Conductance of nano-systems with interactions coupled via conduction electrons: Effect of indirect exchange interactions cond-mat/0605756 toappear 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 S Contact (Fermi) 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 S(U) Fermi 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?The embedding method How can we obtain ? Density MatrixRenormalization Group Embedding + DMRG = exact numerical method. Difficulty: Extension outside d=1 Permanent current of a ring embedding the nanosystem + limit of infinite ring size

  4. 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 Correction:

  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. 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 approximationThe 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 ?(Remember Wasburn et al) U

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

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