We report an angle-resolved photoemission investigation of optimally-doped Ca$_{0.33}$Na$_{0.67}$Fe$_2$As$_2$. The Fermi surface topology of this compound is similar to that of the well-studied Ba$_{0.6}$K$_{0.4}$Fe$_2$As$_2$ material, except for lar
ger hole pockets resulting from a higher hole concentration per Fe atoms. We find that the quasi-nesting conditions are weakened in this compound as compared to Ba$_{0.6}$K$_{0.4}$Fe$_2$As$_2$. As with Ba$_{0.6}$K$_{0.4}$Fe$_2$As$_2$ though, we observe nearly isotropic superconducting gaps with Fermi surface-dependent magnitudes. A small variation in the gap size along the momentum direction perpendicular to the surface is found for one of the Fermi surfaces. Our superconducting gap results on all Fermi surface sheets fit simultaneously very well to a global gap function derived from a strong coupling approach, which contains only 2 global parameters.
We used high-energy resolution angle-resolved photoemission spectroscopy to extract the momentum dependence of the superconducting gap of Ru-substituted Ba(Fe$_{0.75}$Ru$_{0.25}$)$_2$As$_2$ ($T_c = 15$ K). Despite a strong out-of-plane warping of the
Fermi surface, the magnitude of the superconducting gap observed experimentally is nearly isotropic and independent of the out-of-plane momentum. More precisely, we respectively observed 5.7 meV and 4.5 meV superconducting gaps on the inner and outer $Gamma$-centered hole Fermi surface pockets, whereas a 4.8 meV gap is recorded on the M-centered electron Fermi surface pockets. Our results are consistent with the $J_1-J_2$ model with a dominant antiferromagnetic exchange interaction between the next-nearest Fe neighbors.
In order to determine the orbital characters on the various Fermi surface pockets of the Fe-based superconductors Ba$_{0.6}$K$_{0.4}$Fe$_{2}$As$_{2}$ and FeSe$_{0.45}$Te$_{0.55}$, we introduce a method to calculate photoemission matrix elements. We c
ompare our simulations to experimental data obtained with various experimental configurations of beam orientation and light polarization. We show that the photoemission intensity patterns revealed from angle-resolved photoemission spectroscopy measurements of Fermi surface mappings and energy-momentum plots along high-symmetry lines exhibit asymmetries carrying precious information on the nature of the states probed, information that is destroyed after the data symmetrization process often performed in the analysis of angle-resolved photoemission spectroscopy data. Our simulations are consistent with Fermi surfaces originating mainly from the $d_{xy}$, $d_{xz}$ and $d_{yz}$ orbitals in these materials.
