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## Main Question or Discussion Point

The electronic structure of CNT is discussed on the basis of band structure of

graphene. Graphene has a linear dispersion relation:

E = h_cut vF |k|

where k is the 2D wavevector and vF is the Fermi velocity. CNTs are

macroscopic along the axis but have a circumference of atomic dimensions, which

suggests that there will be large states in the axial direction but quantized

circumferential states. this implies that there are allowed transitions between circumferential states such that the movement is in the direction perpendicular to the axial direction of CNT. Therefore the movement is in two dimensions, yet we say CNT is a 1D structure. Why is that the case?

graphene. Graphene has a linear dispersion relation:

E = h_cut vF |k|

where k is the 2D wavevector and vF is the Fermi velocity. CNTs are

macroscopic along the axis but have a circumference of atomic dimensions, which

suggests that there will be large states in the axial direction but quantized

circumferential states. this implies that there are allowed transitions between circumferential states such that the movement is in the direction perpendicular to the axial direction of CNT. Therefore the movement is in two dimensions, yet we say CNT is a 1D structure. Why is that the case?