Interlayer coupling in the superconducting state of iron-based superconductors

High-temperature superconducting paring is generally believed to be mediated by the magnetic fluctuations that mostly occur within the two-dimensional conducting layers (Cu-O, Fe-As, or Fe-Se) in copper oxides, iron pnictides, iron chalcogenides, etc. Here, on the basis of inelastic neutron scattering measurements on a superconducting iron pnictide ${\mathrm{Ca}}_{0.33}{\mathrm{Na}}_{0.67}{\mathrm{Fe}}_2{\mathrm{As}}_2$, we have discovered a highly three-dimensional spin resonance mode with upward V-shape dispersions both in the $ab$ plane and along the $c$ axis. The superconducting gaps exhibit strong $k_z$ modulations involved with significant changes on the size of one hole pocket and the density state of the $d_{z^2}$ orbital of Fe. The resonance dispersions don't always seem confined by the total gaps summed on those imperfectly nesting Fermi sheets. It is demonstrated that the $c$-axis dependence of both the resonance energy and its intensity in iron pnictides can be universally scaled with the distance between two adjacent Fe-As layers ($d$), and the $k_z$ modulation of the gap is also anticorrelated with $d$. These results highlight the role of interlayer coupling in iron-based superconductivity, suggesting that the interlayer pairing may also be driven by magnetic fluctuations under certain spin-orbit couplings.