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We analyze the strong hexagonal warping of the Dirac cone of Bi$_2$Te$_3$ byangle-resolved photoemission. Along $\overline{\Gamma}$$\overline{\rm M}$, thedispersion deviates from a linear behavior meaning that the Dirac cone iswarped outwards and not inwards. We show that this introduces an anisotropy inthe lifetime broadening of the topological surface state which is larger along$\overline{\Gamma}$$\overline{\rm K}$. The result is not consistent withnesting. Based on the theoretically predicted behavior of the ground-state spintexture of a strongly warped Dirac cone, we propose spin-dependent scatteringprocesses as explanation for the anisotropic scattering rates. These resultscould help paving the way for optimizing future spintronic devices usingtopological insulators and controlling surface-scattering processes viaexternal gate voltages.

Anisotropic effect of warping on the lifetime broadening of topological surface states in angle-resolved photoemission from Bi$_2$Te$_3$