Phase diagram of doped BaFe$_2$As$_2$ superconductor under broken C$_4$ symmetry

We developed a minimal multi-orbital tight-binding model with realistic hopping parameters that breaks the symmetry of the point group by lowering it from C$_4$ to D$_{2d}$. The model accurately describes the Fermi surface evolution of the electron, BaFe$_{2-x}$Co$_x$As$_2$, and hole, Ba$_{1-y}$K$_y$Fe$_2$As$_2$, doped compounds. Since in this class of materials the competing superconductivity and co-linear antiferromagnetism rely on the evolution of the Fermi surface with doping, we investigated the phase diagram with a mean-field t-U-V Bogoliubov-de Gennes equation. Our results match the experimental electron-doped phase diagram. Furthermore, the model is in reasonable agreement with the experimental hole-doped part with only one set of t, U and V parameters. The self-consistently calculated superconducting order parameter exhibits s+/-d pairing symmetry in the entire doping range. It is the subtle result of competing interactions in the multi-orbital mean-field Hamiltonian based on the broken C$_4$ symmetry and might be observable in STM and ARPES experiments.