The bulk band structure of Bi$_2$Te$_3$ has been determined by angle-resolved photoemission spectroscopy and compared to first-principles calculations. We have performed calculations using the local density approximation (LDA) of density functional theory and the one-shot $GW$ approximation within the all-electron full-potential linearized augmented-plane-wave (FLAPW) formalism, fully taking into account spin-orbit coupling. Quasiparticle effects produce significant changes in the band structure of bite~when compared to LDA. Experimental and calculated results are compared in the spectral regions where distinct differences between the LDA and $GW$ results are present. Overall a superior agreement with $GW$ is found, highlighting the importance of many-body effects in the band structure of this family of topological insulators.
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