Fig. 4: Dirac fermion-induced integer-quantized vortex-bound states.

a Multi-Gaussian fit for the dI/dV spectrum at the vortex center of Fig. 3f. The red dots are the experimental data, the colored dashed curves are the fitting curves of the vortex-bound states, and the black solid curve is the final fitting result. b The line-cut intensity plot same as the Fig. 3f, with the colored marked lines representing the ZBCP and discrete quantized CBSs at different energies marked by L₀, L_±1, L_±2, L_±3, which are obtained from the multi-Gaussian fittings for all the spectra in Fig. 3g. The solid lines are calculated using E_L/ΔE = n (ΔE = 1.22 meV is the average value of energy level spacing), while n is the number of the energy level. c A histogram of the energy values of all the observed in-gap states with a sampling width of 50 μeV. The horizontal energy scale is normalized by the first-level spacing. d Comparison between the numerically calculated energy eigenvalues of CBSs and experimental values for different angular momenta. e Spatial patterns of vortex-bound states at voltage bias equal to 0, −1.2, −2.4, and −3.6 mV, respectively. The size of the area is scaled by the coherence length ξ₀ (ξ₀ ~ 6 nm for CaKFe₄As₄). f Numerical calculations of the two-dimensional local density of L₀ (MZM), L₋₁, L₋₂, and L₋₃, respectively, which are based on the topological vortex core model. g Comparison between the wave functions of STM results (crosses) and numerical calculations (lines). The experimental spatial profiles of energy states are extracted along the solid lines in b. The intensity of numerical local density of states is rescaled to be comparable to the experimental data.