Physics Of Carbon Nanotubes

M. S. Dresselhaus,1 G. Dresselhaus,2 and R. Saito3

'Department of Electrical Engineering and Computer Science and Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, U.S.A. 2Francis Bitter National Magnet Laboratory, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, U.S.A. "Department of Electronics-Engineering, University of Electro-Communications,

Tokyo 182, Japan

(Received 26 October 1994; accepted 10 February 1995)

Abstract—The fundamental relations governing the geometry of carbon nanotubes are reviewed, and explicit examples are presented. A framework is given for the symmetry properties of carbon nanotubes for both symmorphic and non-symmorphic tubules which have screw-axis symmetry. The implications of symmetry on the vibrational and electronic structure of ID carbon nanotube systems are considered. The corresponding properties of double-wall nanotubes and arrays of nanotubes are also discussed.

Key Words—Single-wall, multi-wall, vibrational modes, chiral nanotubes, electronic bands, tubule arrays.

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