  Topological insulators/semimetals and unconventional iron-based
superconductors have attracted major attentions in condensed matter physics in
the past 10 years. However, there is little overlap between these two fields,
although the combination of topological states and superconducting states will
produce more exotic topologically superconducting states and Majorana bound
states (MBS), a promising candidate for realizing topological quantum
computations. With the progress in laser-based spin-resolved and angle-resolved
photoemission spectroscopy (ARPES) with very high energy- and
momentum-resolution, we directly resolved the topological insulator (TI) phase
and topological Dirac semimetal (TDS) phase near Fermi level ($E_F$) in the
iron-based superconductor Li(Fe,Co)As. The TI and TDS phases can be separately
tuned to $E_F$ by Co doping, allowing a detailed study of different
superconducting topological states in the same material. Together with the
topological states in Fe(Te,Se), our study shows the ubiquitous coexistence of
superconductivity and multiple topological phases in iron-based
superconductors, and opens a new age for the study of high-Tc iron-based
superconductors and topological superconductivity.
