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Carbon Nanotubes

Carbon Nanotubes. Riichiro Saito rsaito@ee.uec.ac.jp http://flex.ee.uec.ac.jp. Carbon Nanotubes. (5,5). Armchair Nanotube. (9,0). Zigzag Nanotube. (6,5). Chiral Nanotube. Solid State Properties of Carbon Nanotubes. Structures and Symmetry Electronic and Phonon Properties

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Carbon Nanotubes

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  1. Carbon Nanotubes Riichiro Saito rsaito@ee.uec.ac.jp http://flex.ee.uec.ac.jp

  2. Carbon Nanotubes (5,5) Armchair Nanotube (9,0) Zigzag Nanotube (6,5) Chiral Nanotube

  3. Solid State Properties of Carbon Nanotubes • Structures and Symmetry • Electronic and Phonon Properties • Raman Intensities • Transport Properties • Magnetic Properties • Applications “Physical Properties of Carbon Nanotubes”, by R. Saito, G. Dresselhaus and M.S. Dresselhaus, Imperial College Press (1998) ISBN 1-86094-093-5

  4. Chiral Vectors : (n,m) • Chiral Vector (equator of nanotube): OA, Ch • Translational Vector of 1D material: OB, T • Unit Cell : OAB’B

  5. Symmetry • Symmorphic (mirror symmetry) • Armchair Nanotube (n,n), n=m • Zigzag Nanotube (n,0), m=0 • Non-Symmorphic (axial chirality) • Zigzag Nanotube (n,m), n≠m Fig: (a) (5,5) armchair, (b) (9,0) zigzag, and (c) (10,5) chiral nanotubes

  6. Diameter and Chiral Angle • Diameter : d • Chiral Angle : θ • zigzag θ=0 • armchair θ=π/6 • chiral 0<θ<π/6

  7. Reciprocal Lattice and Wave Vectors • 1 Dimensional Wave Vectors • Nanotube axis direction • Discrete in Circumferential Direction

  8. π band of graphite Unit Cell, B. Z. Energy Band Zero Gap Semiconductor B A t Electronic Properties of Graphene

  9. Energy Bands of Nanotubes • N one-dimensional bands (5,5) (9,0) (10,0)

  10. Metal or Semiconductor depending on chirality • Density of States • Rule for Metal Nanotube

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