Carbon NanotubesRiichiro Saitorsaito@ee.uec.ac.jphttp://flex.ee.uec.ac.jp

(5,5)(9,0)(6,5)Carbon NanotubesArmchair NanotubeZigzag NanotubeChiral Nanotube

Solid State Properties of Carbon NanotubesStructures and SymmetryElectronic and Phonon PropertiesRaman IntensitiesTransport PropertiesMagnetic PropertiesApplicationsPhysical Properties of Carbon Nanotubes, by R. Saito, G. Dresselhaus and M.S. Dresselhaus, Imperial College Press (1998) ISBN 1-86094-093-5

Chiral Vectors : (n,m)Chiral Vector (equator of nanotube): OA, ChTranslational Vector of 1D material: OB, TUnit Cell : OABB

SymmetrySymmorphic (mirror symmetry)Armchair Nanotube (n,n), n=mZigzag Nanotube (n,0), m=0Non-Symmorphic (axial chirality)Zigzag Nanotube (n,m), nm

Fig: (a) (5,5) armchair, (b) (9,0) zigzag, and (c) (10,5) chiral nanotubes

Diameter and Chiral AngleDiameter : d

Chiral Angle : zigzag =0armchair =/6chiral 0

Reciprocal Lattice and Wave Vectors1 Dimensional Wave VectorsNanotube axis direction

Discrete in Circumferential Direction

Electronic Properties of Graphene band of graphiteUnit Cell, B. Z.Energy BandZero Gap Semiconductor

Energy Bands of NanotubesN one-dimensional bands(5,5)(9,0)(10,0)

Metal or Semiconductor depending on chiralityDensity of StatesRule for Metal Nanotube

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