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

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