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We perform scanning tunneling microscopy/spectroscopy study on the layerediron based superconductor KCa$_2$Fe$_4$As$_4$F$_2$ with a critical temperatureof about 33.5 K. Two types of terminated surfaces are generally observed aftercleaving the samples in vacuum. On one commonly obtained surface, we observe afull gap feature with energy gap values close to 4.6 meV. This type of spectrumshows a clean and uniform full gap in space, which indicates the absence of gapnodes in this superconductor. Quasiparticle interference patterns have alsobeen measured, which show no scattering patterns between the hole and tinyelectron pockets, but rather an intra-band scattering pattern is observedpossibly due to the hole-like $\alpha$ pocket. The Fermi energy of this band isonly 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 magneticfield. On the second type of surface which is rarely obtained, the fully gappedfeature can still be observed on the tunneling spectra, although multiple gapsare obtained either from a single spectrum or separate ones, and the gap valuesdetermined from coherence peaks locate mainly in the range from 4 to 8 meV. Ourresults clearly indicate multiple and nodeless superconducting gap nature inthis layered superconductor KCa$_2$Fe$_4$As$_4$F$_2$, and the superfluid ismainly contributed by the hole-like Fermi surfaces near $\Gamma$ point. Thiswould inspire further consideration on the effect of the shallow and incipientbands near M point, and help to understand the pairing mechanism in this highlylayered iron-based superconductor.

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