LAUSR

We analyze the electronic properties of the recently discovered stoichiometric superconductor CaKFe$_4$As$_4$ by combining an ab initio approach and a projection of the band structure to a lowenergy tight-binding Hamiltonian, based on the maximally localized Wannier orbitals of the 3d Fe states. We identify the key symmetries as well as differences and similarities in the electronic structure between CaKFe$_4$As$_4$ and the parent systems CaFe$_2$As$_2$ and KFe$_2$As$_2$. In particular, we find CaKFe4As4 to have a significantly more quasi-two-dimensional electronic structure than the latter systems. Finally, we study the superconducting instabilities in CaKFe$_4$As$_4$ by employing the leading angular harmonics approximation (LAHA) and find two potential A$_{1g}$-symmetry representation of the superconducting gap to be the dominant instabilities in this system.