Modified group projectors: Tight-binding method

Abstract

The symmetry implantation in the tight-binding method is analysed. A transparent 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 π-bands of single-wall carbon nanotubes: together with the dispersion relations, their assignation by the full symmetry (line group) quantum numbers (linear, helical and angular momenta and parities) is performed and the corresponding symmetry-adapted eigenstates are found. It is argued that these novel quantum numbers prevent conductivity in all but armchair tubes.