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.