Nanocrystalline Nanowires: III. Electrons

Nanocrystalline nanowires (NCNW) are fragments of bulk crystals that are infinite in only one direction and typically have some rotational symmetry around this direction. Electron eigenstates belonging to the symmetry labels (k,m) (wavevector and rotational quantum number) are discussed. The rotational quantum number simplifies discussion of optical properties. For m not equal 0, the +/-m degeneracy allows orbital magnetism. The simplest sensible model which is more complex than a one-dimensional chain is solved. Methods are suggested for incorporating rotational symmetry into preexisting codes with three-dimensional translations.