Bilayer Spliting and Unusual Superconducting Gap in KCa₂Fe₄As₄F₂ Superconductor with Double Fe₂As₂ Layers

We report the first high resolution laser Angle-Resolved Photoemission Spectroscopy(ARPES) measurements on a newly discovered iron based superconductor, KCa₂Fe₄As₄F₂ (K12442) which has the K+-cations connecting double Fe₂As₂ layers separated by the insulating Ca₂F₂ block with a high TC of 34 K at stoichiometric composition. Total five hole like Fermi surfaces are clearly identified around Brillouin zone center Γ(0,0) point and four of them are possible from the bilayer splitting of two Fermi surfaces. A tiny electron like pocket is shown around M(±π,±π) points surrounded by four strong spots with their top just below Fermi level. All the hole like pockets around Γ(0,0) point exhibit nearly isotropic nodeless superconducting gap symmetry but with different gap sizes. Their gap sizes can neither be understood in the simple │cos(k_x)+cos(k_y)│ functional form due to the biggest gap size from one middle Fermi surface, nor be consistent with the so-called quasi-nesting between the Fermi pockets around Γ and M points because of mismatch of Femri pocket size. Our observations provide new information and require new insight to understand the superconductivity mechanism in iron based superconductor.