1 / 31

Kondo effect in a quantum dot without spin

Kondo effect in a quantum dot without spin. Hyun-Woo Lee (Postech) & Sejoong Kim (Postech  MIT). References: H.-W. Lee & S. Kim, cond-mat/0610496 P. Silvestrov & Y. Imry, cond-mat/0609355 V. Kashcheyevs, A. Schiller, A. Aharony, & O. Entin-Wohlman, cond-mat/0610194. Kondo effect.

tirza
Download Presentation

Kondo effect in a quantum dot without spin

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Kondo effect in a quantum dot without spin Hyun-Woo Lee (Postech) & Sejoong Kim (Postech  MIT) References: H.-W. Lee & S. Kim, cond-mat/0610496 P. Silvestrov & Y. Imry, cond-mat/0609355 V. Kashcheyevs, A. Schiller, A. Aharony, & O. Entin-Wohlman, cond-mat/0610194

  2. Kondo effect • Temperature dependence of resistance • Resistance minimum

  3. Before After After Kondo effect (continued)[J. Kondo, Prog. Theor. Phys. ’64] • Scattering by magnetic impurities s-d model

  4. LogT dependence in R(T) (*) 엄종화 Scattering amplitude for a channel of where N : number of d-electrons, N(0) : density of state at EF D : width of conduction electron distribution around EF Jk,q = J where –D < ek, eq < D = 0 otherwise This lnT dependence combined with the phonon contribution (T5 dependence) makes a resistance minimum in R(T).

  5. Kondo effect (continued) • High T vs. low T Kondo singlet Cf. Asymptotic freedom

  6. TK << T일 때, (*) 엄종화 Kondo effect When T << TK, r ~ r0 - cT2 : unitary limit TK ~ T일 때, Hamann expression (Phys. Rev. 1967) For TK > T, take (-) in the equation TK < T, take (+) in the equation

  7. Kondo effect in AuFe(26ppm) wire (*) 엄종화 Hamann expression (Phys. Rev. 1967) From fitting the Hamann expression to r(T), we obtain S = 0.12, TK = 0.99 K. Slope of Kondo resistivity = 0.11 nWcm / (ppm decade K) Concentration of AuFe is estimated by the slope of Dr => 26 ppmin the above figure

  8. Kondo effect in quantum dot

  9. n Vg Quantum dot (QD) • “Metallic” limit ~e2/2C >> kT

  10. Transport through a QD • Orthodox theory of Coulomb blockade • Transport due to charge fluctuations

  11. E>> kT Quantum confinement • Single particle energy quantization

  12. n 0 3 1/2 2 0 1 S=1/2 Vg Even-odd effect • Spin singlet (S=0) vs doublet (S=1/2) • QD with odd n = magnetic impurity ???

  13. c.f. n After Before Vg Kondo effect in QD ? • Hamiltonian • Spin flip via second order processes

  14. Kondo effect in QD w/ odd n  Kondo suppression ofR • Theories • T. K. Ng and P. A. Lee • Phys. Rev. Lett. 61, 1768 (1988) • L. I. Glazman and M. E. Raikh • JETP Lett. 47, 452 (1988) • Experiments • D. Goldhaber-Gordon, H. Shtrikman, D. Mahalu, D. Abush-Magder, U. Meirav, and M. A. Kaster • Nature 391, 156 (1998); Phys. Rev. Lett. 81, 5225 (1998) • S. M. Cronenwett, T. H. Oostercamp, and L. P. Kouwenhoven • Science 281, 540 (1998)

  15. Unitary limit of the Kondo effect in SET [W. G. van der Wiel et al., Science ’00] (*) 엄종화 온도대역: 15 mK – 800 mK G(T) G at Vgl = -413mV shows logarithmic T dependence (inset), and saturates below 90mK (unitary limit) This experiment shows a unitary limit = 2e2/h (GR=GL의 경우) Kondo resonance peak Vgl was fixed at -413mV. VSD was biased between S and D. FWHM

  16. Kondo temperature: TK (*) 엄종화 In Anderson model, ; Costi et al., J. Phys.: Condense. Matter 6, 2519 (1994) TK in Log scale An empirical function ; Goldhaber-Gordon et al., PRL 81, 5225 (1998) : universal functional form of T/TK s is a fit parameter, but is almost constant ~0.2 in the Kondo regime.

  17. Kondo effect in QD w/o spin?

  18. t1L t1R t t t1R t2L Two level QD • QD w/ two single-particle level • Source & Drain • Tunneling • “Spin” ?

  19. Pseudospin for 1=2(=) • Unitary transformations Pseudospin up Pseudospin Pseudospin down

  20. 0 1 2 Schrieffer-Wolf transformation:QD system (Anderson model)  s-d model • Fock space decomposition • Full Hamiltonian • Projection to n=1 Fock space

  21. Effective Hamiltonian Hs-d • Total Hamiltonian • Anisotropic antiferro-exchange • U(1) instead of SU(2) • Pseudomagnetic field Bzeff • (*) For = • SU(2): Jz=J+=J- • Bzeff=0

  22. hz 0 1 2 =+U/2 0 -U/2 Pseudomagnetic field Bzeff • Expectation value • For   >  •  Population switching from level to  level with decreasing 

  23. 0 1 2 =+U/2 0 -U/2 Charge 10 Charge 12 U U Population switching (PS) [Silvestrov & Imry, PRL’00] • Energy renormalization • eff= bare+  (hopping) •  : gate voltage dependent

  24. D D Poor man’s scaling • [1] Fock space decomposition • [2] Full Hamiltonian • [3] Projection to “g” sector of Fock space • New Hamiltonian w/ reduced D • [4] Back to [1] D

  25. Scaling equations • Exchange J’s • Scaling invariant • Integration: Characteristic energy scale (Kondo temperature) • Pseudomagnetic field Bzeff • Integration:

  26. Anisotropic s-d model • Approximation •  Anisotropic s-d model • Exact solution (via Bethe ansatz) available !!! • Tsvelick & Wiegmann, Adv. Phys. 32, 453 (1983)

  27. Conductance at T=0 •  and  scattering states • Friedel sum rule • Landauer-Buttiker formula

  28. Anisotropic s-d model [Tsvelick and Wiegmann, Adv. Phys. (1983)] • Sz=(n-n)/2 vs. hz • G vs. 

  29. 0 1 2 =+U/2 0 -U/2 Cf. Conventional spin Kondo • Conventional spin Kondo • Kondo w/o spin • Correlation-induced resonance [Meden & Marquardt, PRL 96, 146801 (2006)]

  30. w/o degeneracy 1-2 0 • Same Unitary transformation • Additional pseudomagnetic field h • Parallel to z • Shift of CIRs • Perpendicular to z • Asymmetry in CIRs (Fano-like)

  31. Summary • Kondo effect in QD w/o spin • Distinct conductance pattern (cf. spin Kondo in QD) • Future directions • w/o degeneracy • Temperature dependence • Pseudospin & real spin • Real Spin [SU(2)] • Pseudospin [Not SU(2) invariant] • Connection w/ anomalous transmission phase problem ?

More Related