Broken Symmetries in Scanning Tunneling Images of Carbon Nanotubes

Scanning tunneling images of carbon nanotubes frequently show electron distributions which break the local sixfold symmetry of the graphene sheet. We present a theory of these images which relates these anisotropies to the off diagonal correlations in the single particle density matrix, and allows one to extract these correlations from the observed images. The theory is applied to images of the low energy states reflected at the end of a tube or by point defects, and to states propagating on defect free semiconducting tubes. The latter exhibit a novel switching of the anisotropy in the tunneling image with the sign of the tunneling bias.