Spontaneous Breaking of Rotation Symmetry in the Edge States of Zigzag Carbon Nanotubes

Analytical Solutions of the edge states were obtained for the (N, 0) type carbon nanotubes with distorted ending bonds. For N = 5 and N >= 7, it was found that the symmetric edge states are mixed via the distortion to form asymmetric edge eigenstates. The density of the pi electrons in the last carbon layer exhibits axial rotation symmetry breaking explicitly. The distortion modes depend on the Occupation of the edge states, implying thin the symmetry of the electron density at the apex could be changed discontinuously by the external electronic field.