Observation of coexistence of itinerant electronic states and local moments in parents compound superconductor Sr$_{\mathrm{4}}$V$_{\mathrm{2}}$O$_{\mathrm{6}}$Fe$_{\mathrm{2}}$As$_{\mathrm{2}}$

Using variable temperature scanning tunneling spectroscopy (STS) and quasi-particle interference (QPI) analysis, we studied coexistence of itinerant electronic states and local moments in Sr$_{\mathrm{4}}$V$_{\mathrm{2}}$O$_{\mathrm{6}}$Fe$_{\mathrm{2}}$As$_{\mathrm{2}}$. Temperature dependent STS measurements showed Fano resonances resulting from the hybridization between local moments (V) and itinerant electrons (Fe) below 100 K, and the formation of Fano lattice implying collective spin excitations between local moments of V atoms below 50 K. QPI analysis showed replica bands and kink features in Fe-itinerant band, implying the existence of Bosonic modes between Sr$_{\mathrm{2}}$VO$_{\mathrm{3}}$ layers and FeAs layers. Our results show the collective behaviors of itinerant electrons and local moments, and the possibility of local moments contributing to superconductivity.