Neutron spin resonance as a probe of Fermi surface nesting and superconducting gap symmetry in Ba$_{0.67}$K$_{0.33}$(Fe$_{1-x}$Co$_{x}$)$_{2}$As$_{2}$

We use inelastic neutron scattering to study energy and wave vector dependence of the superconductivity-induced resonance in hole-doped Ba$_{0.67}$K$_{0.33}$(Fe$_{1-x}$Co$_{x}$)$_{2}$As$_{2}$ ($x=0,0.08$ with $T_c\approx 37, 28$ K, respectively). In previous work on electron-doped Ba(Fe$_{0.963}$Ni$_{0.037}$)$_2$As$_2$ ($T_N=26$ K and $T_c=17$ K), the resonance is found to peak sharply at the antiferromagnetic (AF) ordering wave vector ${\bf Q}_{\rm AF}$ along the longitudinal direction, but disperses upwards away from ${\bf Q}_{\rm AF}$ along the transverse direction. For hole doped $x=0, 0.08$ without AF order, we find that the resonance displays ring-like upward dispersion away from ${\bf Q}_{\rm AF}$ along both the longitudinal and transverse directions. By comparing these results with calculations using the random phase approximation, we conclude that the dispersive resonance is a direct signature of isotropic superconducting gaps arising from nested hole-electron Fermi surfaces.