Broken Symmetries in Scanning Tunneling Images of Carbon Nanotubes

TL;DR

This paper develops a theory linking anisotropic features in scanning tunneling images of carbon nanotubes to off-diagonal correlations in the electron density matrix, enabling extraction of these correlations from experimental images.

Contribution

It introduces a theoretical framework connecting image anisotropies to electron correlations, applied to various nanotube states, revealing a bias-dependent switching phenomenon.

Findings

Anisotropies relate to off-diagonal density matrix correlations.

Application to end states and defect states in nanotubes.

Discovery of bias-dependent switching of tunneling image anisotropy.

Abstract

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.