First Brillouin Zone

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Electronic Properties of Graphene
Graphene
First Brillouin Zone
Anti-Bonding Orbitals
Bonding Orbitals
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Low energy theory 2D massless Dirac Fermions
Dirac (kp) Hamiltonian
left -handed
right-handed
spin molec. orbital state
Kane and Mele, Ando...
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Curling up the Extra Dimension
ky (2p R) 2p j
kx
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Nanotube Band Structure
See, for example Kane and Mele PRL 78, 1932 (97)
Armchair tube
metallic
zigzag tube
E
E
f
semiconducting
BZ boundary
Verified by STM and transport expts.
Eg 1 eV / dnm
Tans et al., Bockrath et al. (97)
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Copying work of Jie Liu et al. (Duke)
Parallel Device Fabrication - CVD
Flying catalyst growth (Liu group)
Gas flow
catalyst pads
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Nanotube band structure
semiconducting
metal
B gt 0
large bandgap
metal
semiconducting
k
1.0
G (e2/h)

0
-10
0
10
Vgate (V)
Vgate (V)
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Nanotubes Optical Properties
Electroluminescence
Fluorescence Spectroscopy
IBM group Science (03)
Rice group Science (02)
Explosion of Interest in Optoelectronic
Properties !