Kondo Effects in Carbon Nanotubes Master Colloquium
by
Jeppe Vilstrup Holm
Supervisor: Poul Erik Lindelof
Kondo Effects in Carbon Nanotubes Master Colloquium
by
Jeppe Vilstrup Holm
Supervisor: Poul Erik Lindelof
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
Outline
Single wall carbon nanotubes (SWCNT)
Single Wall Carbon Nanotubes
a2 a1 Carbon atom Graphene ~1 nm
One dimensional conductor. Metallic or Semiconducting
Single wall carbon nanotubes (SWCNT)
Quantization effects
Back gate Carbon nanotube Electrode Electrode L~300nm SiO2
(insulator) Conductance quantization: Gmax= 4 e2/h
SWCNT (1nm): Four channels (Rmin= 26 k) Size quantization: E~1/L~ 1 meV
(Wave nature of electron)
Separated energy levels Charge quantization: Uc~e2/C~5 meV
(Particle nature of electron)
Single electron transport E SWCNT E+Uc
Outline
Single wall carbon nanotubes (SWCNT)
Quantization effects
SWCNT quantum dots
Device Fabrication
(a) (b) (c) (d) (e) (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
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
Measurement setup
Back gate Vgate Vsd SWCNT Two voltage knobs:
Source-drain voltage Vsd
Gate voltage
Uc ΔE μs μd Coulomb blockade and single electron tunneling Vg[V] G[e2/h] 2 3 4 5 1 2x Coulomb Blockade Single electron tunneling
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