Theory of Kondo transport through quantum dots equilibrium and nonequilibrium properties

1
Theory of Kondo transport through quantum dots-
equilibrium and non-equilibrium properties
YKIS2004, Kyoto

• Kazuo Ueda
• Institute for Solid State Physics
• University of Tokyo

2
Theory of Fano-Kondo effect of transport
properties through quantum dots

• Isao Maruyama and Kazuo Ueda
• Institute for Solid State Physics
• University of Tokyo

3
Experiments on Kondo transport
D. Goldhaber-Gordon, Hadas Shtrikman, D. Mahalu,
David Abusch-Magder, U. Meirav and M. A. Kastner,
Nature 391 (1998) 156
S. M. Cronenwett, T. H. Oosterkamp, and L. P.
Kouwenhoven, Science 281 (1998) 540
4
Unitarity limit
W. G. van der Wiel, S. De Franceschi, T.
Fujisawa, J. M. Elzerman, S. Tarucha and L. P.
Kouwenhoven, Science 289 (2000) 2105
5
Fano effect through a quantum dot in an
Aharonov-Bohm Interferometer (AB-QD)
K. Kobayashi, H. Aikawa, S. Katsumoto and Y. Iye,
Phys. Rev. Lett. 88 (2002) 256806
6
Fano-Kondo Anti-Resonance in a Quantum Wire with
a Side-Coupled Quantum Dot (T-shaped QD)
M. Sato, H. Aikawa, K. Kobayashi, S. Katsumoto
and Y. Iye, cond-mat/0410062
7
Model for the T-shaped QD
8
Conductance
9
Definition of the Fano parameter q
10
Kondo-resonance and anti-Kondo-resonance
11
(No Transcript)
12
Conductance at high temperatures
13
Crossover from the high temperature regimeto the
low temperature regime
14
Temperature dependence of g (q0)
Anti-Kondo-resonance
15
Temperature dependence of g (q-0.8)
16
Aharonov-Bohm quantum dot (without magnetic flux)
17
Conclusions

• A tight binding model for the T-shaped QD is
  proposed.
• The transmission probability of the model is
  described by the Fano-form with a general Fano
  asymmetric parameter q.
• The conductance shows a crossover from the high
  temperature regime to the low temperature regime.
• TgtTK two Fano-peaks at the Coulomb blockades
  or Coulomb
• dips
• TltTK single structure with the new Fano-Kondo
  plateau,
• gq2/(1q2)
• Numerical calculations for temperature dependence
  of the conductance by the Finite Temperature
  DMRG.
• The conductance of the AB-QD is given by the same
  form.

18
Kondo Transport through Quantum Dots

• Tatsuya Fujii and Kazuo Ueda
• ISSP, University of Tokyo

19
Introduction

• Kondo transport is relevant to a quantum dot
• 88 T.K.Ng et al., 88 L.I.Glazman et al.
• 98 D.Goldhaber-Gordon et al., 98
  S.M.Cronenwett
• 00 W.G.van der Wiel et al.
• New features of the Kondo transport
• nonequilibrium nature
• tunnel current is measured with a finite voltage
  drop

20

• Theoretical studies of the nonequilibrium Kondo
  effect
• 2-nd order perturbation for U 91 S.Hershfield
  et al.
• a single Kondo peak
• remarkably good approximation
• in the equilibrium case
• NCA, EOM, RTA 93 S.Meir et al., 96
  J.Konig et al.
• double Kondo peaks
• observation the splitting of the Kondo
  resonance by three-terminal QD 02
  S. De Franceschi
• the double Kondo peaks seem to be reasonable

21

• Problems
• It is not clear how the double Kondo peaks are
  reflected in the observable G(V)
• NCA Fermi liquid
• Perturbation for U the unitary limit
• Required
• A better theoretical approach to the
  nonequilibrium Kondo effect
• Our study
• Perturbative approach to the nonequilibrium Kondo
  effect
• 4-th order perturbation for U Keldysh
  formalism

22

• a single Kondo peak splits into double peaks
  which lead to appearance of a new
  peak in G(V)
• possible relevance to the 0.7 structure
  in Quantum Point Contact

23
Model

• Quantum dot attached to two leads
• single-level Anderson model with symmetric
  condition
• nonequilibrium state

24
Calculations

• (i) density of states at the dot
• retarded Green function in the
  nonequilibrium state
• tunnel current for the symmetric case
• (ii) differential conductance

25
Perturbation theory based on Keldysh formalism

• Keldysh time path
• self energies the same diagrams as the
  equilibrium case

26

• 2nd order
• 4th order skeleton diagrams
• nonskeleton diagrams
• the Kramers-Kronig relation

27
(No Transcript)
28
(No Transcript)
29

• For all U
• the zero-bias peak
• unitary limit
• For large U
• a new peak appears when

30
Origin of the new peak

• the double Kondo peaks develop when

31
Possible relevance of the present study to the
0.7 structure in Quantum Point Contact

• Quantum Point Contact (QPC)
• narrow constriction in 2DEG
• Quantization of conductance
• ballistic transport through 1D subbands
• 0.7 conductance anomaly

(K.J.Thomas et l., PRL 77 (1996) 135)
Zeeman
in the magnetic field
the 0.7 structure stronger at higher
temperature
electron correlation
but not a ground-state property
32

• Evidence for the Kondo effect concerning the 0.7
  structure
• (S. M. Cronenwett et al., PRL 88 (2002) 226805)
• zero-bias peak splits in a magnetic field
• scaling of conductance
• the scaling factor corresponds to a peak width
• universal nature of the Kondo Effect
• experimental results of QPC
• some hint
• present results for QD

33
S. M. Cronenwett et al., PRL 88 (2002) 226805
34
Summary

• Quantum transport through a dot under a finite
  bias voltage
• 4-th order perturbation theory based on
  the Keldysh formalism
• the single Kondo peak splits into the double
  peaks when
• a new peak appears in the conductance
• Possible relevance of the present study to the
  0.7 structure in QPC
• an experimental support for the new peak