Modeling of electronic density of states for single-wall carbon and boron nitride nanotubes

The electronic density of states is calculated for all possible geometric configurations of single-wall carbon and boron nitride nanotubes. The calculation is based on the numerical differentiation of the two-dimensional dispersion relations for graphite and hexagonal boron nitride. The differentiation is performed for all allowed values of the wave vector using the $\pi$-electron approximation. For the particular carbon nanotubes chosen as examples, a good agreement is demonstrated between the calculated values of energy spacing of the symmetric van Hove singularities in the density of states and the experimental data obtained from the resonance Raman scattering study.