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We report the observation of discrete vortex bound states with the energylevels deviating from the widely believed ratio of 1:3:5 in the vortices of aniron based superconductor KCa2Fe4As4F2 through scanning tunneling microcopy(STM). Meanwhile Friedel oscillations of vortex bound states are also observedfor the first time in related vortices. By doing self-consistent calculationsof Bogoliubov-de Gennes equations, we find that at extreme quantum limit, thesuperconducting order parameter exhibits a Friedel-like oscillation, whichmodifies the energy levels of the vortex bound states and explains why itdeviates from the ratio of 1:3:5. The observed Friedel oscillations of thebound states can also be roughly interpreted by the theoretical calculations,however some features at high energies could not be explained. We attributethis discrepancy to the high energy bound states with the influence of nearbyimpurities. Our combined STM measurement and the self-consistent calculationsillustrate a generalized feature of the vortex bound states in type-IIsuperconductors.

Friedel Oscillations of Vortex Bound States Under Extreme Quantum Limit in KCa2Fe4As4F2