Observation of a ubiquitous three-dimensional superconducting gap function in optimally-doped Ba$_{0.6}$K$_{0.4}$Fe$_2$As$_2$

The iron-pnictide superconductors have a layered structureformed by stacks of FeAs planes from which the superconductivity originates. Given the multiband and quasi three-dimensional \cite{3D_SC} (3D) electronic structure of these high-temperature superconductors, knowledge of the quasi-3D superconducting (SC) gap is essential for understanding the superconducting mechanism. By using the \KZ-capability of angle-resolved photoemission, we completely determined the SC gap on all five Fermi surfaces (FSs) in three dimensions on \BKFAOP samples. We found a marked \KZ dispersion of the SC gap, which can derive only from interlayer pairing. Remarkably, the SC energy gaps can be described by a single 3D gap function with two energy scales characterizing the strengths of intralayer $\Delta_1$ and interlayer $\Delta_2$ pairing. The anisotropy ratio $\Delta_2/\Delta_1$, determined from the gap function, is close to the c-axis anisotropy ratio of the magnetic exchange coupling $J_c/J_{ab}$ in the parent compound \cite{NeutronParent}. The ubiquitous gap function for all the 3D FSs reveals that pairing is short-ranged and strongly constrain the possible pairing force in the pnictides. A suitable candidate could arise from short-range antiferromagnetic fluctuations.