Effect of Band Structure on Quantum Interference

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
CNT-FET is Field Effect Transistor using Carbon Nanotube.
• The nanotube FET is hopeful to be used
as
– Logic circuit,
– Single electron transistor (SET),
– Spin FET.
Carbon Nanotubes
Single wall carbon nanotube (SWNT)
Armchair tube
Zigzag tube
Density of states
Multi wall carbon nanotube
(MWNT)
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
When the gate voltage is negative…
positive…
Au
eh he he he
Insulator
Gate
-+ +
- +
-
CNT
Au
1D Density of States for free electron
systems
1D - Density of States : D1d
1d   D1d d
1d : Number of states
 2k 2

2m
 : Energy k : Wave number
1d  2   2
L
dk

2
ｋ
L1 m

d
  2

2
2 
 d  kdk  
dk 

m
m 

L m 1
 D1d 
 2 
D1d  
  0
DOS of SWNT
(14,14)
DOS (states/unit cell)
(14,0)
Zigzag tube
Armchair tube
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
CNP: Charge neutrality point
300K
The bottom of the curve at 300K
is nearly U gate= -0.2V.
10K The fluctuation at 10K and 1K is
due to the Universal Conductance
Fluctuation (UCF) and the band
1K structure.
The fine fluctuation at 30mK
30mK is due to the Coulomb
Blockade.
Conductance G(U) in Magnetic
fields perpendicular to the tube axis
T=10K
B=0T
U gate =const.
-2
0
2
B （T)
The deviation from the zero-field
conductance
G(U,B)-G(U,B=0)
The Magnetoconductance disappears at
certain gate voltages U*.
U*
The Magnetic fields independence of
conductance G under the gate voltage U*.
U*
U*
U*
-0.2V
These gate voltages U* are grouped
symmetrically around U≒-0.2V.
U*
U*
U*
U* U*
U* U*
U*
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*
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 N* was checked.
U*=U*+0.2 (V)
U*: Singular points in Fig.b
N*: The number of excess
electrons on the tube.
 CU *  eN *
Circles : Present experiment
Triangles : Reference data
Theoretical calculation of the
conductance G

1
2
 e 2   1 WeB 2 
  2 
GWL (U , B )  
①

2
3 
 L   L
L : Phase coherent length of the electrons
W : Diameter of nanotube
L : Length of nanotube
G(U , B)  G(U , B  0)  GWL (U , B)
G (U , B)  G (U , B  0)  G (U , B  0)  GWL (U , B)  G (U , B  0)  GWL (U , B  0)
 GWL (U , B)  GWL (U , B  0)
1



2
2
2




 e  1 WeB 
  2 
 
  L 
2
3 
 L   L



Theoretical calculation of the
conductance G
GWL (U , B)  GWL (U , B  0) G(U,B)-G(U,B=0)
L , G (U , B  0) are
obtainedby fitting
theexperimental
conductance data.
U*
U*
U*
U*
U*
U*
Calculation data
Experimental data
Conclusion
• Phase coherent length L 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.

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