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Numerical study of transport properties of carbon nanotubes. Dhanashree Godbole Brian Thomas Summer Materials Research Training Oakland University 2006. Overview. CNT: The material of the future Structure of Graphene and CNT’s Carbon nanotubes: bands and DOS - PowerPoint PPT Presentation
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Numerical study of transport properties of carbon nanotubes
• Dhanashree Godbole
• Brian Thomas
Summer Materials Research Training
Oakland University 2006
Overview
CNT: The material of the futureStructure of Graphene and CNT’sCarbon nanotubes: bands and DOS Infinite CNT’s to quantum dotsQuantum dots: what and whyNumerical results:
• Coulomb Blockade• Kondo effect
Why Carbon nanotubes?
Amazing electronic and physical properties• Space and mass saving• Strength and durability
The graphene sheet and its band structure
The Graphene Layer
(n,m)
CNT: band structure and DOS
nqka
kaka
n
qtkE aq
2,...,1,
,2
cos42
coscos41)(
2/1
2
An Infinite CNT to finite CNT
DO
S
Finite CNT to Quantum Dot
Artificial atomsTransfer of a single electron charge
Coulomb Blockade
Increased resistance
No conduction Conduction
Kondo Effect
Low-temp. increase in resistanceKondo resonance creates existence of
a new state
Numerical Results: One Level QD
One available state for the electron
-2 -1 0 1 2
0.0
0.2
0.4
0.6
0.8
1.0
-2 -1 0 1 2
0.0
0.2
0.4
0.6
0.8
1.0
G(e
2 /h)
Vg
-2 -1 0 1 2
0.0
0.2
0.4
0.6
0.8
1.0
-2 -1 0 1 2
0.0
0.2
0.4
0.6
0.8
1.0
G(e
2 /h)
Vg
-3 -2 -1 0 1 2
0.0
0.2
0.4
0.6
0.8
1.0
-3 -2 -1 0 1 2
0.0
0.2
0.4
0.6
0.8
1.0
G(e
2 /h)
Vg
CNT as a Quantum dot
Carbon nanotubes have two available states for electrons to propagate in
-3 -2 -1 0 1
0.0
0.5
1.0
1.5
2.0
G(2
e2 /h
)
Vg
-1.6 -1.4 -1.2 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.20.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
G(2
e2 /h
)
Vg
CNT as Quantum dot
B field kills Kondo effect…why?
-3 -2 -1 0 1 2
0.0
0.5
1.0
G(2
e2 /h
)
Vg
-3 -2 -1 0 1
0.0
0.5
1.0
G(2
e2 /h
)
Vg
Experimental Results
-2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.00.0
0.5
1.0
1.5
2.0
3.01.51.0
0.5
G(2e
2/h)
Vg
U=U'=0.5t'=0.2t"=0.0
orb=0.2
sp
=0.04
b0.0
-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
U=U'=0.5t'=0.2t"=0.0E=0.035E
sp
Vg
B
Eorb
orb
=0.2
sp
=0.04
a
Delft University - NetherlandsProf. Leo Kouwenhoven group
Conclusion
What we learned• Basics of quantum mechanics and its
applications in condensed matter physics• First time using computer code and
programming with FORTRAN• Energy dispersion relations and their use in
research of CNTs• Quantum Dots and the use of CNTs as QDs• Modeling and using numerical operations to
represent real systems.
