Effect of Band Structure on Quantum Interference in Multiwall Carbon Nanotubes Reference Bernhard...

Effect of Band Structure on Quantum Interference in

Multiwall Carbon Nanotubes

Reference

Bernhard Stojetz et al. Phys.Rev.Lett. 94, 186802 (2005)

Suzuki-Kusakabe lab

Yoshihisa MINAMIGAWA

Various applications of CNT-FET

• The nanotube FET is hopeful to be used as– Logic circuit,– Single electron transistor (SET),– Spin FET.

CNT-FET is Field Effect Transistor using Carbon Nanotube.

Carbon Nanotubes

Armchair tube

Zigzag tube

Single wall carbon nanotube (SWNT)

Multi wall carbon nanotube

(MWNT)

Density of states

Structure of CNT-FET

Gate

A single nanotube transistor.

A semiconducting nanotube is used.

A single electron transistor built from a single nanotube.

Electric field effect to CNT

CNT

Gate

Insulator

+ + +

eeee

When the gate voltage is positive…

Au Au

- - -

hhhh

When the gate voltage is negative…

1D Density of States for free electron systems

numberWaveEnergy ::2

22

km

k

dkL

d 22 21

ｋ

d

mL

2

1

dk

mkdk

md

22

1

21

mLD d

statesofNumber:1d dD dd 11

01 dD

dD1 : States ofDensity -1D

DOS of SWNT

Zigzag tube Armchair tube

DO

S (

stat

es/u

nit

cell)

(14,0) (14,14)

The purpose of the paper

• This paper reports…

Measurement of conductance of a carbon nanotube under Gate voltage and Magnetic field.

⇒Determination of the Chirality of carbon nanotube by conductance measurement is expected to be possible.

Reference

Bernhard Stojetz et al. Phys.Rev.Lett. 94, 186802 (2005)

Gate voltage U dependence of conductance G

The bottom of the curve at 300K is nearly = -0.2V.300K

10K

1K

30mK

gateU

The fine fluctuation at 30mK is due to the Coulomb Blockade.

CNP: Charge neutrality point

The fluctuation at 10K and 1K is due to the Universal Conductance Fluctuation (UCF) and the band structure.

Conductance G(U) in Magnetic fields perpendicular to the tube axis

-2 20B （ T)

gateU =const.

B=0T

T=10K

The deviation from the zero-field conductance

G(U,B)-G(U,B=0)

U*

U*

U*

U*

U*

U*

-0.2V

U* U* U* U* U* U*

The Magnetoconductance disappears at certain gate voltages U*.

The Magnetic fields independence of conductance G under the gate voltage U*.

These gate voltages U* are grouped symmetrically around U -0.2V.≒

Density of states of SWNT (140,140)

Black line : DOS of SWNT

Gray line : The number of excess electrons on the tube ( N)⊿

When fermi level overlaps van Hove singularity, We expect big change in magnetoconductance when the Fermi level of the nanotube come across the singularity.

Relation of U* and N*⊿ ⊿

** NeUC

To confirm next assumptions

1. The current mainly flows in the outermost tube,

2. The chirality of the tube is given by (140,140),

3. Charge is induced by the gate voltage,

the next relations U* and*was checked.

U*=U*+0.2 (V)

U*: Singular points in Fig.b

N*: The number of excess electrons on the tube.

Circles : Present experiment Triangles : Reference data

Theoretical calculation of the conductance G

①

2

1

2

2

2

2

3

1),(

WeB

LL

eBUGWL

),()0,(),( BUGBUGBUG WL

L : Phase coherent length of the electrons

W : Diameter of nanotube

L : Length of nanotube

LWeB

LL

e

BUGBUG

BUGBUGBUGBUGBUGBUG

WLWL

WLWL

2

1

2

2

2

2

3

1

)0,(),(

)0,()0,(),()0,()0,(),(

Theoretical calculation of the conductance G)0,(),( BUGBUG WLWL G(U,B)-G(U,B=0)

Calculation data Experimental data

data. econductanc

alexperiment the

fittingby obtained

are)0,(, BUGL U*

U*

U*

U*

U*

U*

Conclusion

• Phase coherent length is very short at the onset of a subband. Theoretical explanation is unknown.

• It is expected that deviation from zero-field conductance G(U,B)-G(U,B=0) determines van Hove singularities and structure of the tube.

L