# STM imaging of electronic waves on the surface of Bi$_2$Te$_3$: topologically protected surface states and hexagonal warping effects

## TL;DR

This study uses STM to investigate the surface electronic states of Bi$_2$Te$_3$, confirming topological protection and revealing hexagonal warping effects through LDOS oscillations.

## Contribution

It provides direct STM evidence of topologically protected surface states and identifies hexagonal warping effects in Bi$_2$Te$_3$ surface electronic structure.

## Key findings

- LDOS oscillations are damped near the main surface band, indicating topological protection.
- At higher energies, oscillations with specific wave-vectors suggest hexagonal warping.
- STM results match ARPES data, validating the surface state analysis.

## Abstract

Scanning tunneling spectroscopy studies on high-quality Bi$_2$Te$_3$ crystals exhibit perfect correspondence to ARPES data, hence enabling identification of different regimes measured in the local density of states (LDOS). Oscillations of LDOS near a step are analyzed. Within the main part of the surface band oscillations are strongly damped, supporting the hypothesis of topological protection. At higher energies, as the surface band becomes concave, oscillations appear which disperse with a particular wave-vector that may result from an unconventional hexagonal warping term.