Strongly correlated superconductor with polytypic 3D Dirac points

Topological superconductors should be able to provide essential ingredients for quantum computing, but are very challenging to realize. Spin-orbit interaction in iron-based superconductors opens the energy gap between the $p$-states of pnictogen and $d$-states of iron very close to the Fermi level, and such $p$-states have been recently experimentally detected. Density functional theory predicts existence of topological surface states within this gap in FeTe$_{1-x}$Se$_x$ making it an attractive candidate material. Here we use synchrotron-based angle-resolved photoemission spectroscopy and band structure calculations to demonstrate that FeTe$_{1-x}$Se$_x$ (x=0.45) is a superconducting 3D Dirac semimetal hosting type-I and type-II Dirac points and that its electronic structure remains topologically trivial. We show that the inverted band gap in FeTe$_{1-x}$Se$_x$ can possibly be realized by further increase of Te content, but strong correlations reduce it to a sub-meV size, making the experimental detection of this gap and corresponding topological surface states very challenging, not to mention exact matching with the Fermi level. On the other hand, the $p-d$ and $d-d$ interactions are responsible for the formation of extremely flat band at the Fermi level pointing to its intimate relation with the mechanism of high-T$_c$ superconductivity in IBS.