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Observation of antiphase coherent phonons in the warped Dirac cone of Bi$_2$Te$_3$

In this Rapid Communication we investigate the coupling between excited electrons and phonons in the highly anisotropic electronic structure of the prototypical topological insulator Bi$_2$Te$_3$. Using time- and angle-resolved photoemission spectroscopy we are able to identify the emergence and ultrafast temporal evolution of the longitudinal-optical A$_{1g}$ coherent-phonon mode in Bi$_2$Te$_3$. We observe an antiphase behavior in the onset of the coherent-phonon oscillations between the $\overline{ΓK}$ and the $\overline{ΓM}$ high-symmetry directions that is consistent with warping. The qualitative agreement between our density-functional theory calculations and the experimental results reveals the critical role of the anisotropic coupling between Dirac fermions and phonon modes in the topological insulator Bi$_2$Te$_3$.