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Silvano De Franceschi

Orbital Kondo effect in carbon nanotube quantum dots. Silvano De Franceschi. Laboratorio Nazionale TASC INFM-CNR, Trieste, Italy. http://www.tasc.infm.it/~defranceschis/SilvanoHP.htm. ‘Simple’ and controllable systems can be obtained in nanostructured materials.

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Silvano De Franceschi

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  1. Orbital Kondo effect in carbon nanotube quantum dots Silvano De Franceschi Laboratorio Nazionale TASC INFM-CNR, Trieste, Italy http://www.tasc.infm.it/~defranceschis/SilvanoHP.htm

  2. ‘Simple’ and controllable systems can be obtained in nanostructured materials. => quantum coherent electronics (spintronics, quantum computation, superconducting electronics…) => fundamental quantum phenomena (quantum coherent dynamics, entanglement, strongly correlated systems,…)

  3. Spin ½ Kondo | |

  4. Spin ½ Kondo | | Goldhaber-Gordon et al., Nature (1998) Cronenwett et al., Science (1998) Schmid et al., Physica B (1998) TK ~ 0.1 - 1 K Semiconductor dots Nygard et al., Nature (2000) TK ~ 1 K Carbon nanotube dots Liang et al. & J. Park et al.Nature (2002) TK ~ 10 K Single-molecule dots

  5. TK  Spin ½ Kondo | | In a metal with magnetic impurties: In a quantum dot with spin 1/2

  6. Spin ½ Kondo | | Gate-voltage control: => Kondo effect in the unitary limit (G → 2e2/h) [Science 289, 2105 (2000)] Magnetic-field control: => integer-spin Kondo effect at singlet-triplet degeneracy [Nature 405, 764 (2000)] [ Phys. Rev. Lett. 88, 126803 (2002)] Bias-voltage control: => Kondo effect out of equilibrium [Phys. Rev. Lett. 89, 156801(2002)]

  7. + + Spin ½ Kondo | | Orbital Kondo + |+ |

  8. + + + + Spin ½ Kondo | |  Orbital Kondo + |+ | = |+, |+, SU(4) Kondo |, |, Experiments in 2DEG QDs Theory proposals in 2DEG QDs S. Sasaki et al., Phys. Rev. Lett. (2004)   L. Borda et al.,Phys. Rev. Lett. (2003). G. Zaránd et al.,Solid State Comm. (2003).

  9. Orbital magnetic moment  + v v ^ ^ Periodic boundary conditions: Quantized momentum around circumference  One-dimensional subbands E (k||) k|| () ()

  10. Finite length L  I discrete spectrum: 4-fold shell structure at B=0 (orbital+spin degeneracy)  + v v SWNT ^ ^ Gate VG V Nanotube quantum dot E (k||) k|| E(1) E-(1) () () E(2) E-(2) E(3) E-(3)

  11. I  + v v SWNT ^ ^ Gate VG V E (k||) k|| E(1) Orbital splitting () E-(1) E(2) () E-(2) E(3) B B E-(3) B  0 Nanotube quantum dot discrete spectrum: 4-fold is lifted at B0 (orbital splitting >> spin splitting) [Phys. Rev. Lett. 94, 156802 (2005)] Prediction: Ajiki & Ando, J. Phys. Soc. Jpn (1993)

  12. |, |+, |, |+, Kondo effect in a NT QD with 4-fold shell structure [Nature 434, 484 (2005)] • Four-fold shell structure at B=0 • Each shell has two orbitals with opposite orbital magnetic moment • Orbitals in different shells cross each other at high B E gmB0 B B = 0 B = B0 gmB0 | , > |+, > |, > |+, > |+, > | , > | , > |+, > Intra-shell 4-fold degeneracy Inter-shell 2-fold degeneracy SU(4) Kondo Orbital Kondo

  13. Linear conductance of a small-band-gap CNT QD 3rd SHELL T=8K 2nd SHELL U+D U half of 1st SHELL n = 1 n = 3 n = 2 4 3 B (T) 2 1 0 VG(V)

  14. + v v ^ ^ Orbital magnetic moment orb  0.8 meV/T (>> B = 0.06 meV/T) Consistent with theoretical predictions (Ajiki&Ando J.Phys.Soc. Jpn (1993)) and with recent experiments: Minot et al., Nature (2004); Zaric et al., Science (2004); Coskun et al., ibid. 4 3 B (T) 2 1 0 VG(V)

  15. 800 0.2 7 Vg (mV) G (e2/h) 6 700 0 5 4 600 3 30 2 Vsd (mV) 500 0 1 2 3 4 1 Colour scale x100 -30 0.3 0.4 0.5 0.6 0 3.6 Vg (V) B(T) Orbital magnetic moment E. Minot et al. Nature 428, 536 (2004) They measured large orbital magnetic moments orb = DevF/4 ~ 0.7meV/T ~ 12 B Problems: • No 4-fold degeneracy • No link between spectrum & B-evolution of QD states Small band gap semic. nanotube

  16. + v v ^ ^ Orbital magnetic moment orb  0.8 meV/T (>> B = 0.06 meV/T) Consistent with theoretical predictions (Ajiki&Ando J.Phys.Soc. Jpn (1993)) and with recent experiments: Minot et al., Nature (2004); Zaric et al., Science (2004); Coskun et al., ibid. 4 3 B (T) 2 1 0 VG(V)

  17. QD orbital & spin configuration 1/2 1/2 1 0 0 1/2 1/2 1/2 0 0 D1 G1 F2 F1 E2 C2 E1 B1 C1 D2 1 1 E (k||) k|| E (k||) E(1) E-(1) k|| E(2) E-(2) E(3) E-(3) E(1) E-(1) E(2) E-(2) E(3) E-(3) E (k||) E (k||) E (k||) E (k||) k|| k|| k|| k|| E(1) E(1) E-(1) E-(1) E(1) E(1) E-(1) E(2) E-(1) E(2) E-(2) E-(2) E(2) E(2) E-(2) E-(2) E(3) E(3) E-(3) E-(3) E(3) E-(3) E(3) E-(3) F’ C’ D’ E’ A’ B’ x20 4 3 II IV IV I II I III B(T) 2 1 0 E D F B C A 3.0 3.5 4.0 2.5 VG(V)

  18. QD orbital & spin configuration 1/2 1/2 1 0 0 1/2 1/2 1/2 0 0 G1 F2 F1 B1 C2 E1 E2 D2 C1 D1 1 1 F’ C’ D’ E’ A’ B’ x20 4 3 II IV IV I II I III B(T) 2 1 0 E D F B C A 3.0 3.5 4.0 2.5 VG(V) B E

  19. B E(1) E+(1) AA’ (AA’): ,3 E(2) E+(2) ,2 1 –orb(2)– – gB 2 ,1 E(3) E+(3) +,1 +,3 BB1 B1B’ +,2 , (BB’): 1 orb(2)– – gB 1 E –orb(2)+ – gB D23 D12 2 2 , CC1 C1C2 C2C’ , (CC’): 1 1 orb(2)– – gB 1 –orb(2)+ – gB –orb(1)– – gB 2 2 2 DD1 D1D2 D2D’ , , (DD’): 1 1 1 orb(2) + – gB orb(2)– – gB –orb(1)– – gB 2 2 2 E2E’ EE1 E1E2 , , (EE’): 1 1 –orb(1)+ – gB 1 orb(2)+ – gB –orb(1)– – gB 2 2 2 FF1 F1F2 F2F’ , , (FF’): 1 orb(1)– – gB 1 1 orb(2)+ – gB –orb(1)+ – gB 2 2 2 [Phys. Rev. Lett. 94, 156802 (2005)]

  20. QD orbital & spin configuration 1 electron 3 electrons 1/2 1/2 1 0 0 1/2 1/2 1/2 0 0 F1 B1 C2 D1 D2 G1 E2 F2 C1 E1 1 1 Orbital crossing at B=3T F’ C’ D’ E’ A’ B’ x20 4 3 II IV IV I II I III B(T) 2 1 0 E D F B C A 3.0 3.5 4.0 2.5 VG(V) B E

  21. E gmB0 B=B0 6T B |, |+, Orbital flip |, |+, Orbital Kondo Effect 10 0 1/2 8 1/2 B (T) 6 1 4 1/2 0 1/2 2 I III III IV II II 0 0.95 0.90 VG (V)

  22. B=B0 6T B=B0 6T E B=B0 6T B=B0 6T 2gmB0 2gmB0 |, B 2B 2B |, |+, B B0 Orbital flip Orbital flip at eV=dB |+, |, |+, |+, |, Orbital Kondo Effect E 10 0 gmB0 1/2 8 1/2 B (T) 6 1 4 1/2 0 1/2 2 I III III IV II II 0 0.95 0.90 VG (V) B

  23. Low-impedance bipolar spin filter II II III III I I IV B Switch VG switch filter polarity VG Orbital Kondo effect  low impedance

  24. Orbital+Spin Degeneracy => Strong Kondo (multilevel) 1/2 1/2 1 0 0 1/2 1/2 1/2 0 0 G1 1 1 2.50 2.75 3.00 3.25 3.50 VG (V) 4 3 II IV IV I II I III B(T) 2 1 0 3.0 3.5 4.0 VG(V) 2.5 4 II I III 0 2 IV V (mV) 0 -2 B = 0T -4 • Strong Kondo effect for 1 and 3 electrons in the shell • Strong triplet-singlet inelastic cotunneling peaks for 2 electrons in the shell [S. Sasaki, S. DF et al. Nature (2000)]

  25. Multiple splitting @ finite B ! 4 II I III 0 IV 2 V (mV) B = 0T 0 -2 -4 4 2 B = 1.5T V (mV) 0 -2 -4 2.50 2.75 3.00 3.25 3.50 VG (V) The Kondo resonance for 1 electron splits in 4 peaks

  26. Four-fold splitting  SU(4)-Kondo Orbital splitting dI/dV 2 I 1 Zeeman splitting V (mV) 0 B V -1 -2 -2 -1 0 1 2 B (T) [Theory: Choi, Lopez and Aguado, cond-mat/0411665]

  27. Zeeman, orbital, orbital + Zeeman 0.8 B=80mT 0.4 0.08 V (mV) 0 dI/dV (e2/h) B=0.7T 0.04 -0.4 -0.8 0 1 2 3 0 1 2 3 B (T) B (T) 0.08 gBB dI/dV (e2/h) 0.04 0.5 0 -0.5  eV= +DE V (mV) 4orbB 2gBB eV= -DE Inelastic cotunneling spectroscopy [PRL 86, 878 (2001)] DE Step in dI/dV at V=level spacing 2 V (mV) 0 -2 -1.21 -1.19 VG (V)

  28. References Orbital Kondo effect[Nature 434, 484 (2005)] Magneto-transport spectroscopy[Phys. Rev. Lett. 94, 156802 (2005)] Collaborators Pablo Jarillo-Herrero Jing Kong Herre van der Zant Cees Dekker Leo Kouwenhoven

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