Transcript Slide 1

Nano-Optics Journal Club
June 26, 2006
Andy Walsh
“Orbital Kondo effect in carbon nanotubes”
Pablo Jarillo-Herrero, Jing Kong, Herre S.J. van der Zant,
Cees Dekker, Leo P. Kouwenhoven, Silvano De Franceschi
Kavli Institute of Nanoscience, Delft University of Technology, The Netherlands
Nature, Vol 434, 484, 24 March 2005
Outline
- Good news / bad news
- What are coulomb oscillations ?
- What is the Kondo effect ?
- SU(4) Kondo
- Other types of Kondo
- Experimental results
Good News / Bad News
Good News
- Kondo turns out to be an area of intense interest in nanophysics
- It’s pretty cool…
Bad News
- I might have bit off more than I can chew with this one…
So More Good News !
- No long derivations !
Coulomb Blockade
Insulating “Island”
Γl
Metal Contacts
Tunneling Barriers
Γr
Positive Vg applied
“Coulomb Oscillations” – conductance oscillations with gate voltage
http://en.wikipedia.org
Shell Filling and Level Repulsion
Hund’s rule
Ref 9
Anderson Model
Magnetic Impurity in a Metal
Ref 1
Theory
“The Kondo effect concerns the interaction of a localized spin
with a Fermi sea of electrons. It is a crucial effect in various
areas of nanophysics where often a nano-sized object with
spin is in close proximity to a metal.”2
Singlet coupling of
impurity spin to fermi
sea of electron spins
SU(2) Kondo
Singlet state formation
leads to peak in DOS at EF
“Co-tunneling event”
Requires a net magnetic moment on the impurity site to couple to the fermi sea
Several relevant energy scales: Γ, U, kbTk , Δ
Low temperature effect i.e. T < “Tk”
Ref 9
SU(4) Kondo
Circular QD
Carbon NT
Ref 8
4 e- Coulomb Oscillations
(1) CVD CNT growth on p+ Si substrate with Fe
(2) NT identification relative to lithographic marks
(3) e-beam lithography to pattern electrodes
followed by e-beam evaporation
B = 0 Tesla
B = 9 Tesla
Ref 6
SU(4) Kondo
Enhanced Kondo effect / increased Tk
Orbital Kondo
High Transmission
Spin filter !
+ orbital
- orbital
↑ spin
↓ spin
Kondo Ridges
+ orbital
- orbital
↑ spin
↓ spin
Multiple Kondos
Ref 8
Logarithmic Temperature Dependence of the Conductance
ρ α ln(1/T)
B=0
T = 8K down to ~500 mK
Why no ρ divergence as T → 0 then?
Large Parameter Space
Γl
Γr
Conductance ( V, Vg, B, T, Γl , Γr )
Orbital Kondo
Conductance Ridges
Results
ST Kondo
Conductance Ridge
SU(4) Kondo
25 mK
1.1 K
Results
B=0T
B=0T
4-Fold
Splitting
B = 1.5 T
gμbB / kbTk
gμorbB / kbTk
eV / kbTk
Summary
- Kondo effect arises from singlet coupling of the magnetic
moment of an impurity to electron spins in a metal which leads
to conductance, via co-tunneling processes, when coulomb
blockade would normally predict much smaller or even zero
conductance.
- Definitive demonstration of Kondo enhanced conductance
as evidenced by logarithmic increase of resistance with
decreasing temperature
- Demonstration of SU(4) Kondo, ST Kondo, TLS Kondo
- Tk approaching 10K due to enhanced degeneracy
Additional References
1. A. Castro-Neto, PY 741-2 Notes, Ch 10 (2004).
2. Govorov et al, PRB 67, 241307 (2003).
3. Jun Kondo AIST website
http://www.aist.go.jp/aist_j/information/emeritus_advisor/JK-achievements.html
4. Goldhaber-Gordon et al, Nature 391, 156-159 (1998).
5. Jarillo-Herrero et al, arXiv, 0411440 (2004).
6. Liang et al, PRL 88, 126801 (2002).
7. Nygard et al, Nature 408, 342-346 (2000).
8. Potok and Goldhaber-Gordon, Nature 434, 451-452 (2005).
9. Sasaki and Tarucha, J. Phys. Soc. Japan 74, 88-94 (2005).
10. De Franceschi et al, PRL 86, 878-881 (2001)
Questions?
Coulomb Diamond
Ref 10
Theory
“Professor Kondo found that the scattering probability of an electron from a
localized magnetic spin within the metal exhibits anomalous behavior. It increases
logarithmically with the inverse temperature, due to contributions from third-order
perturbation theory in which the dynamical nature of the spin was first taken into
account. In combination with the scattering probability due to phonons, which
decreases with lowering temperature, this behavior gives rise to a minimum in the
total scattering rate as the temperature varies.”
“The Kondo theory triggered many theoretical and experimental studies, which
indicated that the Kondo effect is not simply a property of dilute magnetic alloys
but a fundamental property of many-body systems, relevant to many areas of
physical science including particle physics. The first issue was how to reconcile
the logarithmic divergence as absolute zero is approached with the finite value
observed. This problem was tackled by leading theorists, who thereby generated
powerful theoretical methods and discovered interesting new physics. They found
that at very low temperatures a bound state is formed between the localized spin
and conduction electrons, which causes the spin to vanish and suppresses the
logarithmic divergence.”3
Theory
Ref 6
Theory
Ref 7