The effect of As-Chain layers in CaFeAs${}_2$

The new discovered iron-based superconductors have chain-like As layers. These layers generate an additional 3-dimensional hole pocket and cone-like electron pockets. The former is attributed to the Ca $d$ and As1 $p_z$ orbitals and the latter are attributed to the anisotropic Dirac cone, contributed by As1 $p_x$ and $p_y$ orbitals. We find that large gaps on these pockets open in the collinear antiferromagnetic ground state of CaFeAs${}_2$, suggesting that the chain-like As layers are strongly coupled to FeAs layers. Moreover due to the low symmetry crystal induced by the As layers, the bands attributed to FeAs layers in $k_y=\pi$ plane are two-fold degenerate but in $k_x=\pi$ plane are lifted. This degeneracy is protected by a hidden symmetry $\widehat{\mathrm{{\rm Y}}}=\widehat{T}{\widehat{R}}_y$. Ignoring the electron cones, the materials can be well described by a six-band model, including five Fe $d$ and As1 $p_z$ orbitals. We suggest that these new features may help us to identify the sign change and pairing symmetry in iron based superconductors.