Problem about electronic structure

[davidpotter]

Hello everyone!
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?

 

[DrDu]

There are no truly one dimensional structures in nature, so this always has to be understood as kind of an approximation. Namely, if the radius of the CNT (I suppose you mean carbon nanotubes -- if you expect an answer, it would be really wise to spell out your abbreviations once) is small, the corresponding excitations will be relatively high energy. So on energy scales small compared to these energies, you will only have to control the motion in one dimension.