Broken symmetries in scanning tunneling images of carbon nanotubes

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Abstract
Scanning tunneling images of carbon nanotubes frequently show electron distributions that break the local sixfold symmetry of the graphene sheet. We present a theory of these images that 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 switching of the anisotropy in the tunneling image with the sign of the tunneling bias.
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