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 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 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 c topological superconductivity.High-T c iron-based superconductors feature multiple bands near E F , which enhances the difficulty in understanding the details of unconventional pairing 1-3 . It, however, also allows for a wealth of, possibly topologically non-trivial, electronic bands, of which a recent example is the TI states discovered in the ironbased superconductor Fe(Te,Se) 4 , hinting at a promising direction to realize topological superconductivity and MBSs 5-9 . In view of Fe(Te,Se), a pressing subsequent question is to which extent this marks a generic phe-nomenon in different classes of iron-based high-T c superconductors. In this work, we find that the emergence of non-trivial topological bands near the Fermi level is indeed a common feature of various iron-based superconductors. Our first-principles calculations reveal that BaFe 2 As 2 , LiFeAs and Fe(Te,Se) all exhibit band inversions along k z . To confirm these calculations, the band structures of Li(Fe,Co)As and Fe(Te,Se) were investigated by laser-based high-resolution ARPES. Firstly, we observe that TI bands reminiscent of Fe(Te,Se) exist in Li(Fe,Co)As as well, supporting the generic existence of non-trivial topology in iron-based superconductors. Secondly and more interestingly, we predict and observe TDS bands in Li(Fe,Co)As and Fe(Te,Se), which we investigate via high-resolution ARPES, spin-resolved ARPES (SARPES), and magnetoresistance (MR) measurements. Finally, we discuss the phase diagram of these topological high-T c compounds as a function of Fermi level (doping). The combination of topological states and superconductivity may produce not only surface topological superconductivity deriving from the TI edge states, but also bulk topological superconductivity from the TDS bands.Normal insulator (NI), TI, and TDS constitute topologically disti...

The iron-based superconductor is emerging as a promising platform for Majorana zero mode, which can be used to implement topological quantum computation. One of the most significant advances of this platform is the appearance of large vortex level spacing that strongly protects Majorana zero mode from other low-lying quasiparticles. Despite the advantages in the context of physics research, the inhomogeneity of various aspects hampers the practical construction of topological qubits in the compounds studied so far. Here we show that the stoichiometric superconductor LiFeAs is a good candidate to overcome this obstacle. By using scanning tunneling microscopy, we discover that the Majorana zero modes, which are absent on the natural clean surface, can appear in vortices influenced by native impurities. Our detailed analysis reveals a new mechanism for the emergence of those Majorana zero modes, i.e. native tuning of bulk Dirac fermions. The discovery of Majorana zero modes in this homogeneous material, with a promise of tunability, offers an ideal material platform for manipulating and braiding Majorana zero modes, pushing one step forward towards topological quantum computation.