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Conductance Through Coupled Quantum Dots Study

Investigating conductance in quantum dots based on coupled dot structures using advanced theoretical methods. Analysing Kondo regimes, adding FM coupling, and comparing results from NRG, CPMC, and GS methods.

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Conductance Through Coupled Quantum Dots Study

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  1. Conductance through coupled quantum dots J. Bonča Physics Department, FMF, University of Ljubljana, J. Stefan Institute, Ljubljana, SLOVENIA

  2. Collaborators: • R. Žitko, J. Stefan Inst., Ljubljana, Slovenia • A.Ramšak and T. Rejec,FMF, Physics dept., University of Ljubljana and J. Stefan Inst., Ljubljana, Slovenia

  3. Introduction • Experimental motivation • Single QD: using three different methods: NRG, CPMC and GS – accurate results in a wide parameter regime • DQD system: • Large td: Kondo regimes for odd DQD occupancy • Small td: Two-stage Kondo regime • Adding FM coupling • Three QD’s: • Good agreement between CPMC and GS. • Two regimes • t’’>G: three peaks in G(d) due to 3 molecular levels • t’’<G: a single peak in G(d) of width ~ U

  4. Double- and multiple- dot structures Holleitner et el., Science 297, 70 (2002) Craig et el., Science 304, 565 (2004)

  5. Quantum Dot(Anderson single impurity problem) d

  6. ed+U ed Quantum Dot U=1 d d=ed+U/2

  7. ed+U ed Quantum Dot U=1 d

  8. ed+U ed Quantum Dot U=1 d

  9. ed+U ed Quantum Dot U=1 d

  10. ed+U ed Quantum Dot U=1 d

  11. ed+U ed Quantum Dot U=1 d

  12. ed+U ed Quantum Dot U=1 d

  13. ed+U ed Quantum Dot U=1 d d=ed+U/2 Meir-Wingreen, PRL 68,2512 (1992)

  14. ed+U ed Quantum Dot U=1 d d=ed+U/2

  15. ed+U ed Quantum Dot U=1 d d=ed+U/2

  16. ed+U ed Quantum Dot U=1 d d=ed+U/2

  17. ed+U ed Quantum Dot U=1 d d=ed+U/2

  18. ed+U ed Quantum Dot U=1 d d=ed+U/2

  19. ed+U ed Quantum Dot U=1 d D=U>>G d=ed+U/2 ~ gate voltage

  20. Three alternative methods: • Constrained Path Monte Carlomethod(CPMC),Zhang, Carlson and Gubernatis, PRL 74 ,3652 (1995);PRB 59, 12788 (1999). • Projection – variational metod (GS), Schonhammer, Z. Phys. B 21, 389 (1975); PRB 13, 4336 (1976), Gunnarson and Shonhammer, PRB 31, 4185 (1985), Rejec and Ramšak, PRB 68, 035342 (2003). • Numerical Renormalization Group using Reduced Density Matrix (NRG), Krishna-murthy, Wilkins and Wilson, PRB 21, 1003 (1980); Costi, Hewson and Zlatić, J. Phys.: Condens. Matter 6, 2519, (1994); Hofstetter, PRL 85, 1508 (2000).

  21. How to obtain G from GS properties: • CPMC and GS are zero-temperature methods  Ground state energy • Conditions: System is a Fermi liquid ~ N-(noninteracting) sites, N ∞ ~ G0=2e2/h Rejec, Ramšak, PRB 68, 035342 (2003)

  22. Comparison: CPMC,GS,NRG • CPMC, • GS-variational, • Hartree-Fock: • NRG: U<t; Wide-band Meir-Wingreen, PRL 68,2512 (1992)

  23. Comparison: CPMC,GS,NRG • CPMC, • GS-variational, • Hartree-Fock: • NRG: U>>t; Narrow-band Meir-Wingreen, PRL 68,2512 (1992)

  24. Side-coupled Double Quantum Dot

  25. Large td

  26. Large td – Widths of conductance plateaus: Energies on isolated DQD: d2 d1

  27. Large td – Kondo temperatures: Estimating TK using Scrieffer-Wolf:

  28. Large td – Kondo temperatures: Estimating TK using Scrieffer-Wolf:

  29. ES=1 ES=0 Large td – Adding FM coupling -Jad

  30. Small td – Two-stage Kondo effect Vojta et al., PRB 65, 140405 (2002); Hofstetter, Schoeller, PRL 88, 016803 (2002), Cornaglia and Grempel, PRB 71, 075305 (2005), Wiel et al., PRL 88, 126803 (2002). Jeff<TK:Two Kondo temperatures: TK and TK0 Two energy scales: Jeff=4td2/U, TK Jeff<TK TK0 TK

  31. Small td – Two-stage Kondo effect Jeff>TK Jeff w 0 0.25 0.5

  32. Small td – Two-stage Kondo effect Jeff~TK TK TK0 w 0 0.25 0.5

  33. Small td – Two-stage Kondo effect TK0 Jeff<TK TK w 0 0.25 0.5

  34. Small td – Two-stage Kondo effect Jeff<TK~T TK Experimental evidence Wiel et al., PRL 88, 126803 (2002). w 0 0.25 0.5

  35. Large td – Adding FM coupling Two-stage Kondo effect? Voja et al., PRB 65, 140405 (2002), Hofstetter, Schoeller, PRL 88, 016803 (2002),

  36. Three coupled quantum dots • Using CPMC: NCPMC [100,180] • Using GS – variational: NGS [1000,2000]

  37. Three coupled QDs 1 2 3 Oguri, Nisikawa,Hewson, cond-mat/0504771

  38. Conclusions • Using three different methods: NRG, CPMC and GS – accurate results in a wide parameter regime • DQD system: • Large td: Kondo regimes for odd DQD occupancy (analytical expressions for TK and widh G(d)) • Small td: Two-stage Kondo regime (analytical expressions for TK0) • Three QD’s: • Good agreement between CPMC and GS. • Two regimes • t’’>G: three peaks in G(d) due to 3 molecular levels • t’’<G: a single peak in G(d) of width ~ U

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