Hydrostatic-pressure induced phase transition of phonons in single-walled nanotubes

We study the effect of the hydrostatic pressure on the phonons in single-walled carbon nanotubes (SWNTs) in a magnetic field. We calculate the magnetic moments of the phonons using a functional integral technique, and find that the phonons in SWNTs undergo a pressure-induced phase transition from the paramagnetic phase to the diamagnetic phase under hydrostatic pressure 2 GPa. We explain the mechanism of generating this phase transition.