Detailed theoretical study of the electro-optical properties of helically coiled carbon nanotubes (CNTs) is presented. Electronic band structure and density of states as well as optical absorption spectra are calculated for fully relaxed structures and for the structures subjected to the tensile strain. It is shown that according to the conducting properties helically coiled CNTs can be classified as quasi-metals, semi-metals or semiconductors (with direct or indirect band gap). Under the strain band gap narrowing and ultimate band gap closing is predicted, while no change of the conducting properties of the metallic tubes is expected, according to our calculations. As for the optical absorption the situation is quite the opposite: metallic helically coiled CNTs response substantially in contrast to the semiconducting tubes.
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