Breakdown of 2mm symmetry in electron diffraction from multiwalled carbon nanotubes

Electron diffraction patterns of single-walled carbon nanotubes always have 2mm symmetry regardless if the nanotubes themselves have such symmetry. We here show that, for the case of multiwalled carbon nanotubes, the 2mm symmetry can break down when coherent interferences of the electron waves from two different shells take place such as when two shells of the same helicity but their chiral indices (u,v) have opposite evenness/oddity. Both an experimental electron diffraction pattern and analytic analysis are presented to demonstrate the conditions under which the 2mm symmetry breaks down in the electron diffraction patterns of multiwalled carbon nanotubes.