1. If you re-use any material in this presentation, please credit: Michael S. Fuhrer, University of Maryland

2. Why is Carbon Unique for Electronics? C - - - - CarbonGraphite 4 valence electrons 1 p z orbital 3 sp 2 orbitals Fundamental question: Is graphite a metal or a semiconductor? Hexagonal lattice; 1 p z orbital at each site

3. Solid State Physics in One Dimension 1 atom 1 electron 1 orbital (doubly degenerate) Energy Levels: Ground state: Fill lowest five (doubly degenerate) levels Excited state; Energy ε above ground state “metallic” ε Ten atoms:

4. Solid State Physics in One Dimension 1 atom 1 electron 1 orbital (doubly degenerate) Energy Levels: Dimerization creates two bands Electrons fill lower band “semiconducting” EgEg Dimerization can lower energy: Excited state costs energy E g

5. Graphite: Atoms or Dimers? Atomic chain: metallic Dimer chain: semiconducting Graphite: Metallic in some directions, Semiconducting in others!

6. Rolling up graphene into a tube… Pick a lattice vector in graphite Cut out a strip perpendicular to that vector Roll up the strip to form a tube! Graphics courtesy Rick Smalley

7. Nanotubes: Metallic or Semiconducting? Metallic Semiconducting …depends on how nanotube is wrapped. Whether nanotube is metallic or semiconducting…

8. Nanotube Band Structure k r R = n (integer) Momentum around circumference is quantized krkr Metal Semiconductor E k 3Δ 0 -3Δ E k 2Δ Δ 0 -Δ -2Δ Δ ~ 350 meV/[d(nm)] v F ~ 9.3 x 10 7 cm/s E 2 = (ħv F k) 2 E 2 = Δ 2 + (ħv F k) 2