Single particle tunneling spectroscopy and superconducting gaps in layered iron based superconductor KCa$_{2}$Fe$_{4}$As$_{4}$F$_{2}$

We perform scanning tunneling microscopy/spectroscopy study on the layered iron based superconductor KCa$_2$Fe$_4$As$_4$F$_2$ with a critical temperature of about 33.5 K. Two types of terminated surfaces are generally observed after cleaving the samples in vacuum. On one commonly obtained surface, we observe a full gap feature with energy gap values close to 4.6 meV. This type of spectrum shows a clean and uniform full gap in space, which indicates the absence of gap nodes in this superconductor. Quasiparticle interference patterns have also been measured, which show no scattering patterns between the hole and tiny electron pockets, but rather an intra-band scattering pattern is observed possibly due to the hole-like $\alpha$ pocket. The Fermi energy of this band is only about $24\pm6$ meV as derived from the energy dispersion result. Meanwhile, impurity induced bound-state peaks can be observed at about $\pm2.2$ meV on some spectra, and the peak value seems to be independent to magnetic field. On the second type of surface which is rarely obtained, the fully gapped feature can still be observed on the tunneling spectra, although multiple gaps are obtained either from a single spectrum or separate ones, and the gap values determined from coherence peaks locate mainly in the range from 4 to 8 meV. Our results clearly indicate multiple and nodeless superconducting gap nature in this layered superconductor KCa$_2$Fe$_4$As$_4$F$_2$, and the superfluid is mainly contributed by the hole-like Fermi surfaces near $\Gamma$ point. This would inspire further consideration on the effect of the shallow and incipient bands near M point, and help to understand the pairing mechanism in this highly layered iron-based superconductor.

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