A distinct electronic structure was observed in the single-layer FeSe which shows surprisingly high-temperature superconductivity over 65 K. Here, we demonstrate that the electronic structure can be explained by the effective strain effect due to substrates. More importantly, we find that this electronic structure can be tuned into robust topological phases from a topologically trivial metallic phase by the spinorbital interaction and couplings to substrates. The topological phase is robust against any perturbations that preserve the time-reversal symmetry. Our study suggests that nontrivial topology and high-T c superconductivity can be intertwined in the single FeSe layer to search novel physics.

Although iron-based superconductors are multiorbital systems with complicated band structures, we demonstrate that the low-energy physics which is responsible for their high-T c superconductivity is essentially governed by an effective two-orbital Hamiltonian near half filling. This underlying electronic structure is protected by the S 4 symmetry. With repulsive or strong next-nearest-neighbor antiferromagnetic exchange interactions, the model results in a robust A 1g s-wave pairing which can be mapped exactly to the d-wave pairing observed in cuprates. The classification of the superconducting (SC) states according to the S 4 symmetry leads to a natural prediction of the existence of two different phases, named the A and B phases. In the B phase, the superconducting order has an overall sign change along the c axis between the top and bottom As (or Se) planes in a single Fe-As (or Fe-Se) trilayer structure, the common building block of iron-based superconductors. The sign change is analogous to the sign change in the d-wave superconducting state of cuprates upon 90 rotation. Our derivation provides a unified understanding of iron pnictides and iron chalcogenides, and suggests that cuprates and iron-based superconductors share an identical high-T c superconducting mechanism.