Spectroscopic evidence for topological band structure in FeTe$_{0.55}$Se$_{0.45}$

FeTe$_{0.55}$Se$_{0.45}$(FTS) occupies a special spot in modern condensed matter physics at the intersections of electron correlation, topology, and unconventional superconductivity. The bulk electronic structure of FTS is predicted to be topologically nontrivial thanks to the band inversion between the $d_{xz}$ and $p_z$ bands along $\Gamma$-$Z$. However, there remain debates in both the authenticity of the Dirac surface states (DSS) and the experimental deviations of band structure from the theoretical band inversion picture. Here we resolve these debates through a comprehensive ARPES investigation. We first observe a persistent DSS independent of $k_z$. Then, by comparing FTS with FeSe which has no band inversion along $\Gamma$-$Z$, we identify the spectral weight fingerprint of both the presence of the $p_z$ band and the inversion between the $d_{xz}$ and $p_z$ bands. Furthermore, we propose a reconciling band structure under the framework of a tight-binding model preserving crystal symmetry. Our results highlight the significant influence of correlation on modifying the band structure and make a strong case for the existence of topological band structure in this unconventional superconductor.