Kondo Effects in Carbon Nanotubes

1
Kondo Effects in Carbon Nanotubes

• Master Colloquium
• by
• Jeppe Vilstrup Holm
• Supervisor Poul Erik Lindelof

2
Outline

• Single wall carbon nanotubes (SWCNT)
• Quantization effects
• SWCNT quantum dots
• The Kondo effect in bulk
• Kondo effects in carbon nanotubes
• Equilibrium
• In equilibrium
• Conclusion

3
Outline

• Single wall carbon nanotubes (SWCNT)

4
Single Wall Carbon Nanotubes
Graphene
Carbon atom
1 nm
a2
a1
5
One dimensional conductor.Metallic or
Semiconducting
Metallic if 2nm/3q
Metallic
Semiconducting
Metallic
6
Outline

• Single wall carbon nanotubes (SWCNT)
• Quantization effects

7
Carbon nanotube
L300nm
Electrode
Electrode
?EUc
Back gate
SiO2 (insulator)
?E
SWCNT
Conductance quantization Gmax 4 e2/h SWCNT
(1nm) Four channels (Rmin 26 k?)
Charge quantization Uce2/C5 meV (Particle
nature of electron) Single electron transport
Size quantization ?E1/L 1 meV (Wave nature of
electron) Separated energy levels
8
Outline

• Single wall carbon nanotubes (SWCNT)
• Quantization effects
• SWCNT quantum dots

9
Device Fabrication
(c)
(a)
(b)
(e)
(d)
(a) Alignment marks made using lithography and
metal evaporation
(b) Catalyst islands made using lithography and
material spinning
(c) Grow SWCNT by chemical vapour deposition
(d) Electrodes made using electron beam
lithography and metal evaporation
(e) Bonding pads made using optical lithography
and metal evaporation
10
Cryogenics measurements at low temperature
Low temperature is needed to observe these
quantum phenomena
4K Helium bath (4He) 300mK Heliox Closed
liquid/gas system (3He) 30mK Kelvinox 3He/4He
dilution refrigerator
11
Measurement setup
Vsd
SWCNT
Back gate
Vgate

• Two voltage knobs
• Source-drain voltage Vsd
• Gate voltage

12
Coulomb blockade and single electron tunneling
Ge2/h
3
4
5
1
2
VgV
?E
2x
Uc
µs
µd
Coulomb Blockade
Single electron tunneling
13
?E
Uc
Uc
VsdmV
Uc/(ea)
3
2
1
5
4
?E
eVsd
Uc
µd
White High dI/dV (increase in current) Black
Low dI/dV
14
Outline

• Single wall carbon nanotubes (SWCNT)
• Quantization effects
• SWCNT quantum dots
• The Kondo effect in bulk

15
Kondo effect causes increased resistivity at low
temperatures
16
Kondo Effect in bulkKondo cloud at low
temperature
17
Outline

• Single wall carbon nanotubes (SWCNT)
• Quantization effects
• SWCNT quantum dots
• The Kondo effect in bulk
• Kondo effects in carbon nanotubes
• Equilibrium (Zero bias)

18
Kondo effect with odd occupancy on tube
Spin on Tube
Kondo Cloud in Electrodes
19
Spin flipping proces
Odd
Odd
Odd
Odd
x
x
x
x
Even
Even
Even
Even
(c)
(a)
(b)
?t h/Uc
Uc
20
Extra peak in density of states
N is odd
N is even
Gs
Gd
Gs
Gd
2kBTK
µs
µd
µs
µd
e0
e0
G
G
G Gs Gd
21
(a)
Even
Even
Even
Odd
Odd
Odd
Odd
Even
Ge2/h
(b)
VsdmV
VgV
22
(c)
Ge2/h
TK
23
Outline

• Single wall carbon nanotubes (SWCNT)
• Quantization effects
• SWCNT quantum dots
• The Kondo effect in bulk
• Kondo effects in carbon nanotubes
• Equilibrium
• In equilibrium (finite bias)

24
Kondo effect with even occupancy on tube
Even
Even
Even
Odd
Odd
Odd
Odd
Odd
Gateswitch
Even
Odd
eV ?
eV
?
25
Extra peak in density of states
eV lt ?,d
eV ?,d
Odd
Even
eV
eV
G
G
26
Cotunneling
I
dI/dV
V
V
Kondo Effect
I
dI/dV
V
V
27
(No Transcript)
28
Conclusions

• SWCNT quantum dots devices
• Coulomb blockade
• Kondo effects
• Equilibrium
• In equilibrium