  Topological insulators and semimetals as well as unconventional iron-based
superconductors have attracted major recent attention in condensed matter
physics. Previously, however, little overlap has been identified between these
two vibrant fields, even though the principal combination of topological bands
and superconductivity promises exotic unprecedented avenues of superconducting
states and Majorana bound states (MBSs), the central building block for
topological quantum computation. Along with progressing laser-based
spin-resolved and angle-resolved photoemission spectroscopy (ARPES) towards
high energy and momentum resolution, we have resolved topological insulator
(TI) and topological Dirac semimetal (TDS) bands near the Fermi level
($E_{\text{F}}$) in the iron-based superconductors Li(Fe,Co)As and Fe(Te,Se),
respectively. The TI and TDS bands can be individually tuned to locate close to
$E_{\text{F}}$ by carrier doping, allowing to potentially access a plethora of
different superconducting topological states in the same material. Our results
reveal the generic coexistence of superconductivity and multiple topological
states in iron-based superconductors, rendering these materials a promising
platform for high-$T_{\text{c}}$ topological superconductivity.

Superconductivity;Materials Science;Strongly Correlated Electrons