We report on a theoretical study of the electronic and optical properties of freestanding, [0001] oriented wurtzite GaN nanowires and nanotubes based on an atomistic tight binding approach. The developments of band structure, optical properties, and effective mass are studied as functions of nanowire size. It is shown that the valence band structure of the nanowire depends on the lateral size of the nanowire and that the order between the first two valence bands is reversed above a critical size. The fundamental optical transition is found to be strong for nanowire sizes below, and weak for nanowire sizes above, this critical size. The first strong optical transition is found to have a very large optical polarization anisotropy with the dominant component parallel to the nanowire axis. It is also shown that there is a simple functional relationship between the conduction band effective mass and the subband energy, while no such general relation can be found for the valence bands. For the nanotubes the change in energy compared to the solid nanowire is found to be strongly related to the distribution of the original nanowire state wave function. The incorporation of a hole in the nanowire will force a change in the ordering between the first two valence band states compared to a below critical size nanowire.

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