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Conductance of a spin-1 QD: two-stage Kondo effect

Conductance of a spin-1 QD: two-stage Kondo effect. Anna Posazhennikova Institut für Theoretische Festkörperphysik, Uni Karlsruhe, Germany. Collaborators: Babak Bayani (TFP, University Karlsruhe, Germany) Piers Coleman (Rutgers University, NJ, USA).

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Conductance of a spin-1 QD: two-stage Kondo effect

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  1. Conductanceof a spin-1 QD:two-stage Kondo effect Anna Posazhennikova Institut für Theoretische Festkörperphysik, Uni Karlsruhe, Germany Collaborators: Babak Bayani (TFP, University Karlsruhe, Germany) Piers Coleman (Rutgers University, NJ, USA) Les Houches, June 19, 2006

  2. Outline • Introduction: Kondo effect in bulk and mesoscopic systems • Spin-1 QD: theoretical expectations • Model and T-matrix analysis • Conductance calculations • Conclusions and outlook

  3. Introduction: Kondo Effect

  4. History of Kondo effect System: metallic host + magnetic impurity • 1930 – ρmin in some alloys • 1950 – Χcurie –measurements showed that a LM forms in those alloys, which exhibit ρmin Q1: why does LM form? • 1961 - P. W. Anderson: U is large enough compared to interlevel spacing Atomic limit of Anderson model Possible states

  5. History of Kondo effect Q2: why does the formation of LM lead to ρmin ? • 1964 – Jun Kondo, Hamiltonian • Perturbation theory breaks down at TK • TK is the only scale in the problem • Q3: why does ρ saturates at low temperatures? • 1970 – conjecture of Anderson and Yuval – • GS is a paramagnetic spin singlet confirmed by • 1971 - K.Wilson – NRG • Up to here: orbital momentum

  6. History of Kondo effect Q4: what happens in more realistic situation with • 1980 Blandin, Nozieres • 1984 Andrei, Tsvelik, Wiegman Perfectly Screened KE Underscreened KE Overscreened KE FL NFL NFL USK, OSK – inaccessible in bulk materials Mesoscopics?

  7. Introduction: Kondo Effect in Quantum Dots

  8. Introduction: Kondo Effect in QD

  9. Realization of spin-1 QD: singlet-triplet transition in zero magnetic field Neven Nodd

  10. Spin-1 QD: two-channel Kondo effect Set up: spin, coupled to left (L) and right (R) leads L R Kondo Hamiltonian diagonalization J1, J2 – two coupling constants => two screening channels

  11. Conductance of a spin-1 QD: one-channel => two channel crossover Pustilnik, Glazman, PRL’01

  12. Reminder: Hubbard-Stratonovich transformation Kondo Model Anderson Model Schrieffer-Wolff transformation 2 channel Anderson H-an (infinite U)

  13. Auxiliary particle representation of the Anderson Hamiltonian Introduce auxiliary particles Schwinger bosons auxiliary fermions (holons) + constraint

  14. Novel large-N approximation

  15. T-matrix for one channel for different temperatures and at finite voltage

  16. Conductance of a spin-1 QD: expectations (reminder) One-channel Two-channel Log correction due to USK!

  17. Current through the dot Follow method proposed by Meir, Wingreen, PRL 1992 -Keldysh Green‘s functions

  18. Current throught the dot Single-channel contributions + interference term Goal:calculation of the dot‘s Green‘s functions D

  19. One-channel current Note: the dot GF is proportional to the t-matrix of conduction electrons

  20. Results: conductance – one channel Linear conductance Voltage-dependence of conductance

  21. Results: conductance two-channel QD Everything is messed up by the interchannel GFs => the current is not expressed In terms of t-matrices of single channels Simplifications: linear conductance – elastic scattering => results TK2/TK1 3 1 – 10 2 – 100 3 – 1000 2 1

  22. Comparison with NRG Hofstetter, Schoeller, PRL 2002 NRG gives qualitatively same results

  23. Conclusions and future work • We calculated analytically transport in a spin-1 QD in case of one and two-channels • In case of one –channel singular conductance is obtained – signature of US Kondo effect • In case of two-channels interference effects are observed – conductance is suppressed at low T • Future projects • Improve the results for two-channel conductance, taking into account • the inelastic scattering terms • Inclusion of magnetic field • Inclusion of spin – relaxation effects

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