Electronic excitations in nanoscale systems with helical symmetry

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Abstract
A complete set of helically symmetric wave functions is constructed and is used to set up the Bloch-like states for describing the electronic band structure of nanoscale systems with helical symmetry. Various helical arrangements leading to different graphitic tubules may be obtained by rolling the two-dimensional honeycomb lattice into a cylinder subjected to appropriate periodic boundary conditions. A discussion of the symmetries of these helices is given. This method is applied to study the electronic structure of graphitic tubules and is compared with other methods found in the literature.