Topological surface states and phase transition in BaTh2Fe4As4(N1−xOx)2 superconductors

We perform density functional theory and density functional theory plus dynamical mean-field theory calculations to study the electronic structures and topological properties of iron-based superconductors ${\mathrm{BaTh}}_{2}{\mathrm{Fe}}_{4}{\mathrm{As}}_{4}{({\mathrm{N}}_{1\ensuremath{-}x}{\mathrm{O}}_{x})}_{2}$ ($x=0.1$, 0.2, and 0.3). Taking into account electronic correlation corrections, we find that at small oxygen dopings ($x=0.1$ and 0.2), the ${\mathrm{BaTh}}_{2}{\mathrm{Fe}}_{4}{\mathrm{As}}_{4}{({\mathrm{N}}_{1\ensuremath{-}x}{\mathrm{O}}_{x})}_{2}$ superconductors have nontrivial band topology and Dirac-cone type topological surface states around the Fermi level on the (001) surface, which indicates that they can harbor Majorana zero modes on the (001) surface. Increasing the oxygen doping level, the ${\mathrm{BaTh}}_{2}{\mathrm{Fe}}_{4}{\mathrm{As}}_{4}{({\mathrm{N}}_{1\ensuremath{-}x}{\mathrm{O}}_{x})}_{2}$ superconductor undergoes a topological phase transition between $x=0.2$ and 0.3, and has trivial band topology and no topological surface states on the (001) surface at $x=0.3$. The coexistence of high-temperature superconductivity, topological surface states, and topological phase transition in ${\mathrm{BaTh}}_{2}{\mathrm{Fe}}_{4}{\mathrm{As}}_{4}{({\mathrm{N}}_{1\ensuremath{-}x}{\mathrm{O}}_{x})}_{2}$ superconductors makes them potential platforms to study topological superconductivity, Majorana zero modes and effects induced by a topological phase transition.