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

Abstract

We report the observation of discrete vortex bound states with the energy levels deviating from the widely believed ratio of 1:3:5 in the vortices of an iron based superconductor KCa2Fe4As4F2 through scanning tunneling microcopy (STM). Meanwhile Friedel oscillations of vortex bound states are also observed for the first time in related vortices. By doing self-consistent calculations of Bogoliubov-de Gennes equations, we find that at extreme quantum limit, the superconducting order parameter exhibits a Friedel-like oscillation, which modifies the energy levels of the vortex bound states and explains why it deviates from the ratio of 1:3:5. The observed Friedel oscillations of the bound states can also be roughly interpreted by the theoretical calculations, however some features at high energies could not be explained. We attribute this discrepancy to the high energy bound states with the influence of nearby impurities. Our combined STM measurement and the self-consistent calculations illustrate a generalized feature of the vortex bound states in type-II superconductors.

arXiv comment5 pages, 4 figures

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• Charge Density Wave order and electron-phonon coupling in ternary superconductor Bi${}_2$Rh${}_3$Se${}_2$
• Ultrafast Optical Spectroscopy Evidence of Pseudogap and Electron-Phonon Coupling in an Iron-Based Superconductor KCa${}_2$Fe${}_4$As${}_4$F${}_2$
• Single particle tunneling spectroscopy and superconducting gaps in layered iron based superconductor KCa${}_2$Fe${}_4$As${}_4$F${}_2$
• Near zero-energy Caroli-de Gennes-Matricon vortex states in the presence of impurities
• Pseudogap and Strong Pairing Induced by Incipient and Shallow Bands in the Quasi-Two-Dimensional KCa${}_2$Fe${}_4$As${}_4$F${}_2$
• Coherent coupling between vortex bound states and magnetic impurities in 2D layered superconductors
• Identifying Majorana vortex modes via non-local transport
• Tuning Bound States of Symmetry-Breaking Vortices via Unidirectional Charge Density Wave in a Transition-Metal Dichalcogenide Superconductor
• Necklace-like pattern of vortex bound states
• Mirror-protected Majorana zero modes in $f$-wave multilayer graphene superconductors
• Superconductivity and vortex structure on Bi${}_2$Te${}_3$/FeTe${}_{0.55}$Se${}_{0.45}$ heterostructures with different thickness of Bi${}_2$Te${}_3$ films
• Angular momentum of vortex-core Majorana zero modes
• Quantized bound states around a vortex in anisotropic superconductors
• Non-Hermitian Lindhard function and Friedel oscillations