Peierls instability due to the interaction of electrons with both acoustic and optical phonons in metallic carbon nanotubes

We consider Peierls instability due to the interaction of electrons with both acoustic and optical phonons in metallic carbon nanotubes, resulting in a static twist in the nanotube lattice below the critical temperature T-c. We study lattice excitations, the so-called solitwiston and polartwiston, over the ordered Peierls state for different types of boundary conditions. Furthermore, we calculate the electrical resistivity and find that our theory offers a possible explanation for the observed low-temperature rise in the electrical resistivity of carbon nanotubes.