  Iron-based superconductors offer an ideal platform for studying topological
superconductivity and Majorana fermions. In this paper, we carry out a
comprehensive study of the band topology and topological surface states of a
number of iron-based superconductors using a combination of density functional
theory (DFT) and dynamical mean field theory. We find that the strong
electronic correlation of Fe 3d electrons plays a crucial role in determining
the band topology and topological surface states of iron-based superconductors.
Electronic correlation not only strongly renormalizes the bandwidth of Fe 3d
electrons, but also shifts the band positions of both Fe 3d and As/Se p
electrons. As a result, electronic correlation moves the DFT-calculated
topological surface states of many iron-based superconductors much closer to
the Fermi level, which is crucial for realizing topological superconducting
surface states and observing Majorana zero modes as well as achieving practical
applications, such as quantum computation. More importantly, electronic
correlation can change the band topology and make some iron-based
superconductors topologically nontrivial with topological surface states
whereas they have trivial band topology and no topological surface states in
DFT calculations. Our paper demonstrates that it is important to take into
account electronic correlation effects in order to accurately determine the
band topology and topological surface states of iron-based superconductors and
other strongly correlated materials.
