Modified group projectors: tight-binding method

The symmetry implantation in the tight-binding method is analysed. A transp arent algorithm is proposed to calculate eigenvalues and eigenvectors with automatic assignation by the complete set of conserved quantum numbers. For crystals, the energy bands are obtained with no summation over the lattice , while the eigenvectors are symmetry-adapted generalized Bloch states. The method is applied to the electronic pi-bands of single-wall carbon nanotub es: together with the dispersion relations, their assignation by the full s ymmetry (line group) quantum numbers (linear, helical and angular momenta a nd parities) is performed and the corresponding symmetry-adapted eigenstate s are found. It is argued that these novel quantum numbers prevent conducti vity in all but armchair tubes.