Electronic structure of deformed carbon nanotubes

Electronic structure of deformed carbon nanotubes varies widely depending on their chirality and deformation mode. We present a framework to analyze these variations by quantifying the dispersion relation and density of states. The theory is based on the Huckel tight-binding model and confirmed by four orbital tight-binding simulations of nanotubes under stretching, compression, torsion, and bending. It unriddles and unifies previous band gap studies and predicts the shifting, merging, and splitting of Van Hove singularities in the density of state, and the zigzag pattern of band gap change with strains. Possible applications to nanotube devices and spectroscopy research are also presented.